[WIP] Port of Simon Tatham's Puzzle Collectionpuzzles

Original revision: 5123b1bf68777ffa86e651f178046b26a87cf2d9

MIT Licensed. Some games still crash and others are unplayable due to
issues with controls. Still need a "real" polygon filling algorithm.

The following games are at least partially broken for various reasons:

Cube:     crash with certain settings
Galaxies: crash
Inertia:  crash
Keen:     input issues
Loopy:    weird stuff happens
Map:      crash on input
Mines:    weird stuff happens on target
Palisade: input issues
Signpost: crash on input
Solo:     input issues
Towers:   input and drawing issues
Train Tracks: drawing issues
Twiddle:  weird animation on target
Undead:   input and drawing issues
Unequal:  input and drawing issues
Untangle: input issues

All in all, about 40% of the games are at least partially broken.

Change-Id: I7c69b6860ab115f973c8d76799502e9bb3d52368

1 files changed, 2198 insertions, 0 deletions

diff --git a/apps/plugins/puzzles/unfinished/group.c b/apps/plugins/puzzles/unfinished/group.c
new file mode 100644
index 0000000..bec826e
--- /dev/null
+++ b/apps/plugins/puzzles/unfinished/group.c
@@ -0,0 +1,2198 @@
+/*
+ * group.c: a Latin-square puzzle, but played with groups' Cayley
+ * tables. That is, you are given a Cayley table of a group with
+ * most elements blank and a few clues, and you must fill it in
+ * so as to preserve the group axioms.
+ *
+ * This is a perfectly playable and fully working puzzle, but I'm
+ * leaving it for the moment in the 'unfinished' directory because
+ * it's just too esoteric (not to mention _hard_) for me to be
+ * comfortable presenting it to the general public as something they
+ * might (implicitly) actually want to play.
+ *
+ * TODO:
+ *
+ *  - more solver techniques?
+ *     * Inverses: once we know that gh = e, we can immediately
+ * 	 deduce hg = e as well; then for any gx=y we can deduce
+ * 	 hy=x, and for any xg=y we have yh=x.
+ *     * Hard-mode associativity: we currently deduce based on
+ * 	 definite numbers in the grid, but we could also winnow
+ * 	 based on _possible_ numbers.
+ *     * My overambitious original thoughts included wondering if we
+ * 	 could infer that there must be elements of certain orders
+ * 	 (e.g. a group of order divisible by 5 must contain an
+ * 	 element of order 5), but I think in fact this is probably
+ * 	 silly.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+#include <ctype.h>
+#include <math.h>
+
+#include "puzzles.h"
+#include "latin.h"
+
+/*
+ * Difficulty levels. I do some macro ickery here to ensure that my
+ * enum and the various forms of my name list always match up.
+ */
+#define DIFFLIST(A) \
+    A(TRIVIAL,Trivial,NULL,t) \
+    A(NORMAL,Normal,solver_normal,n) \
+    A(HARD,Hard,NULL,h) \
+    A(EXTREME,Extreme,NULL,x) \
+    A(UNREASONABLE,Unreasonable,NULL,u)
+#define ENUM(upper,title,func,lower) DIFF_ ## upper,
+#define TITLE(upper,title,func,lower) #title,
+#define ENCODE(upper,title,func,lower) #lower
+#define CONFIG(upper,title,func,lower) ":" #title
+enum { DIFFLIST(ENUM) DIFFCOUNT };
+static char const *const group_diffnames[] = { DIFFLIST(TITLE) };
+static char const group_diffchars[] = DIFFLIST(ENCODE);
+#define DIFFCONFIG DIFFLIST(CONFIG)
+
+enum {
+    COL_BACKGROUND,
+    COL_GRID,
+    COL_USER,
+    COL_HIGHLIGHT,
+    COL_ERROR,
+    COL_PENCIL,
+    COL_DIAGONAL,
+    NCOLOURS
+};
+
+/*
+ * In identity mode, we number the elements e,a,b,c,d,f,g,h,...
+ * Otherwise, they're a,b,c,d,e,f,g,h,... in the obvious way.
+ */
+#define E_TO_FRONT(c,id) ( (id) && (c)<=5 ? (c) % 5 + 1 : (c) )
+#define E_FROM_FRONT(c,id) ( (id) && (c)<=5 ? ((c) + 3) % 5 + 1 : (c) )
+
+#define FROMCHAR(c,id) E_TO_FRONT((((c)-('A'-1)) & ~0x20), id)
+#define ISCHAR(c) (((c)>='A'&&(c)<='Z') || ((c)>='a'&&(c)<='z'))
+#define TOCHAR(c,id) (E_FROM_FRONT(c,id) + ('a'-1))
+
+struct game_params {
+    int w, diff, id;
+};
+
+struct game_state {
+    game_params par;
+    digit *grid;
+    unsigned char *immutable;
+    int *pencil;		       /* bitmaps using bits 1<<1..1<<n */
+    int completed, cheated;
+    digit *sequence;                   /* sequence of group elements shown */
+
+    /*
+     * This array indicates thick lines separating rows and columns
+     * placed and unplaced manually by the user as a visual aid, e.g.
+     * to delineate a subgroup and its cosets.
+     *
+     * When a line is placed, it's deemed to be between the two
+     * particular group elements that are on either side of it at the
+     * time; dragging those two away from each other automatically
+     * gets rid of the line. Hence, for a given element i, dividers[i]
+     * is either -1 (indicating no divider to the right of i), or some
+     * other element (indicating a divider to the right of i iff that
+     * element is the one right of it). These are eagerly cleared
+     * during drags.
+     */
+    int *dividers;                     /* thick lines between rows/cols */
+};
+
+static game_params *default_params(void)
+{
+    game_params *ret = snew(game_params);
+
+    ret->w = 6;
+    ret->diff = DIFF_NORMAL;
+    ret->id = TRUE;
+
+    return ret;
+}
+
+const static struct game_params group_presets[] = {
+    {  6, DIFF_NORMAL, TRUE },
+    {  6, DIFF_NORMAL, FALSE },
+    {  8, DIFF_NORMAL, TRUE },
+    {  8, DIFF_NORMAL, FALSE },
+    {  8, DIFF_HARD, TRUE },
+    {  8, DIFF_HARD, FALSE },
+    { 12, DIFF_NORMAL, TRUE },
+};
+
+static int game_fetch_preset(int i, char **name, game_params **params)
+{
+    game_params *ret;
+    char buf[80];
+
+    if (i < 0 || i >= lenof(group_presets))
+        return FALSE;
+
+    ret = snew(game_params);
+    *ret = group_presets[i]; /* structure copy */
+
+    sprintf(buf, "%dx%d %s%s", ret->w, ret->w, group_diffnames[ret->diff],
+	    ret->id ? "" : ", identity hidden");
+
+    *name = dupstr(buf);
+    *params = ret;
+    return TRUE;
+}
+
+static void free_params(game_params *params)
+{
+    sfree(params);
+}
+
+static game_params *dup_params(const game_params *params)
+{
+    game_params *ret = snew(game_params);
+    *ret = *params;		       /* structure copy */
+    return ret;
+}
+
+static void decode_params(game_params *params, char const *string)
+{
+    char const *p = string;
+
+    params->w = atoi(p);
+    while (*p && isdigit((unsigned char)*p)) p++;
+    params->diff = DIFF_NORMAL;
+    params->id = TRUE;
+
+    while (*p) {
+	if (*p == 'd') {
+	    int i;
+	    p++;
+	    params->diff = DIFFCOUNT+1; /* ...which is invalid */
+	    if (*p) {
+		for (i = 0; i < DIFFCOUNT; i++) {
+		    if (*p == group_diffchars[i])
+			params->diff = i;
+		}
+		p++;
+	    }
+	} else if (*p == 'i') {
+	    params->id = FALSE;
+	    p++;
+	} else {
+	    /* unrecognised character */
+	    p++;
+	}
+    }
+}
+
+static char *encode_params(const game_params *params, int full)
+{
+    char ret[80];
+
+    sprintf(ret, "%d", params->w);
+    if (full)
+        sprintf(ret + strlen(ret), "d%c", group_diffchars[params->diff]);
+    if (!params->id)
+        sprintf(ret + strlen(ret), "i");
+
+    return dupstr(ret);
+}
+
+static config_item *game_configure(const game_params *params)
+{
+    config_item *ret;
+    char buf[80];
+
+    ret = snewn(4, config_item);
+
+    ret[0].name = "Grid size";
+    ret[0].type = C_STRING;
+    sprintf(buf, "%d", params->w);
+    ret[0].sval = dupstr(buf);
+    ret[0].ival = 0;
+
+    ret[1].name = "Difficulty";
+    ret[1].type = C_CHOICES;
+    ret[1].sval = DIFFCONFIG;
+    ret[1].ival = params->diff;
+
+    ret[2].name = "Show identity";
+    ret[2].type = C_BOOLEAN;
+    ret[2].sval = NULL;
+    ret[2].ival = params->id;
+
+    ret[3].name = NULL;
+    ret[3].type = C_END;
+    ret[3].sval = NULL;
+    ret[3].ival = 0;
+
+    return ret;
+}
+
+static game_params *custom_params(const config_item *cfg)
+{
+    game_params *ret = snew(game_params);
+
+    ret->w = atoi(cfg[0].sval);
+    ret->diff = cfg[1].ival;
+    ret->id = cfg[2].ival;
+
+    return ret;
+}
+
+static char *validate_params(const game_params *params, int full)
+{
+    if (params->w < 3 || params->w > 26)
+        return "Grid size must be between 3 and 26";
+    if (params->diff >= DIFFCOUNT)
+        return "Unknown difficulty rating";
+    if (!params->id && params->diff == DIFF_TRIVIAL) {
+	/*
+	 * We can't have a Trivial-difficulty puzzle (i.e. latin
+	 * square deductions only) without a clear identity, because
+	 * identityless puzzles always have two rows and two columns
+	 * entirely blank, and no latin-square deduction permits the
+	 * distinguishing of two such rows.
+	 */
+	return "Trivial puzzles must have an identity";
+    }
+    if (!params->id && params->w == 3) {
+	/*
+	 * We can't have a 3x3 puzzle without an identity either,
+	 * because 3x3 puzzles can't ever be harder than Trivial
+	 * (there are no 3x3 latin squares which aren't also valid
+	 * group tables, so enabling group-based deductions doesn't
+	 * rule out any possible solutions) and - as above - Trivial
+	 * puzzles can't not have an identity.
+	 */
+	return "3x3 puzzles must have an identity";
+    }
+    return NULL;
+}
+
+/* ----------------------------------------------------------------------
+ * Solver.
+ */
+
+static int solver_normal(struct latin_solver *solver, void *vctx)
+{
+    int w = solver->o;
+#ifdef STANDALONE_SOLVER
+    char **names = solver->names;
+#endif
+    digit *grid = solver->grid;
+    int i, j, k;
+
+    /*
+     * Deduce using associativity: (ab)c = a(bc).
+     *
+     * So we pick any a,b,c we like; then if we know ab, bc, and
+     * (ab)c we can fill in a(bc).
+     */
+    for (i = 1; i < w; i++)
+	for (j = 1; j < w; j++)
+	    for (k = 1; k < w; k++) {
+		if (!grid[i*w+j] || !grid[j*w+k])
+		    continue;
+		if (grid[(grid[i*w+j]-1)*w+k] &&
+		    !grid[i*w+(grid[j*w+k]-1)]) {
+		    int x = grid[j*w+k]-1, y = i;
+		    int n = grid[(grid[i*w+j]-1)*w+k];
+#ifdef STANDALONE_SOLVER
+		    if (solver_show_working) {
+			printf("%*sassociativity on %s,%s,%s: %s*%s = %s*%s\n",
+			       solver_recurse_depth*4, "",
+			       names[i], names[j], names[k],
+			       names[grid[i*w+j]-1], names[k],
+			       names[i], names[grid[j*w+k]-1]);
+			printf("%*s  placing %s at (%d,%d)\n",
+			       solver_recurse_depth*4, "",
+			       names[n-1], x+1, y+1);
+		    }
+#endif
+		    if (solver->cube[(x*w+y)*w+n-1]) {
+			latin_solver_place(solver, x, y, n);
+			return 1;
+		    } else {
+#ifdef STANDALONE_SOLVER
+			if (solver_show_working)
+			    printf("%*s  contradiction!\n",
+				   solver_recurse_depth*4, "");
+			return -1;
+#endif
+		    }
+		}
+		if (!grid[(grid[i*w+j]-1)*w+k] &&
+		    grid[i*w+(grid[j*w+k]-1)]) {
+		    int x = k, y = grid[i*w+j]-1;
+		    int n = grid[i*w+(grid[j*w+k]-1)];
+#ifdef STANDALONE_SOLVER
+		    if (solver_show_working) {
+			printf("%*sassociativity on %s,%s,%s: %s*%s = %s*%s\n",
+			       solver_recurse_depth*4, "",
+			       names[i], names[j], names[k],
+			       names[grid[i*w+j]-1], names[k],
+			       names[i], names[grid[j*w+k]-1]);
+			printf("%*s  placing %s at (%d,%d)\n",
+			       solver_recurse_depth*4, "",
+			       names[n-1], x+1, y+1);
+		    }
+#endif
+		    if (solver->cube[(x*w+y)*w+n-1]) {
+			latin_solver_place(solver, x, y, n);
+			return 1;
+		    } else {
+#ifdef STANDALONE_SOLVER
+			if (solver_show_working)
+			    printf("%*s  contradiction!\n",
+				   solver_recurse_depth*4, "");
+			return -1;
+#endif
+		    }
+		}
+	    }
+
+    return 0;
+}
+
+#define SOLVER(upper,title,func,lower) func,
+static usersolver_t const group_solvers[] = { DIFFLIST(SOLVER) };
+
+static int solver(const game_params *params, digit *grid, int maxdiff)
+{
+    int w = params->w;
+    int ret;
+    struct latin_solver solver;
+#ifdef STANDALONE_SOLVER
+    char *p, text[100], *names[50];
+    int i;
+#endif
+
+    latin_solver_alloc(&solver, grid, w);
+#ifdef STANDALONE_SOLVER
+    for (i = 0, p = text; i < w; i++) {
+	names[i] = p;
+	*p++ = TOCHAR(i+1, params->id);
+	*p++ = '\0';
+    }
+    solver.names = names;
+#endif
+
+    ret = latin_solver_main(&solver, maxdiff,
+			    DIFF_TRIVIAL, DIFF_HARD, DIFF_EXTREME,
+			    DIFF_EXTREME, DIFF_UNREASONABLE,
+			    group_solvers, NULL, NULL, NULL);
+
+    latin_solver_free(&solver);
+
+    return ret;
+}
+
+/* ----------------------------------------------------------------------
+ * Grid generation.
+ */
+
+static char *encode_grid(char *desc, digit *grid, int area)
+{
+    int run, i;
+    char *p = desc;
+
+    run = 0;
+    for (i = 0; i <= area; i++) {
+	int n = (i < area ? grid[i] : -1);
+
+	if (!n)
+	    run++;
+	else {
+	    if (run) {
+		while (run > 0) {
+		    int c = 'a' - 1 + run;
+		    if (run > 26)
+			c = 'z';
+		    *p++ = c;
+		    run -= c - ('a' - 1);
+		}
+	    } else {
+		/*
+		 * If there's a number in the very top left or
+		 * bottom right, there's no point putting an
+		 * unnecessary _ before or after it.
+		 */
+		if (p > desc && n > 0)
+		    *p++ = '_';
+	    }
+	    if (n > 0)
+		p += sprintf(p, "%d", n);
+	    run = 0;
+	}
+    }
+    return p;
+}
+
+/* ----- data generated by group.gap begins ----- */
+
+struct group {
+    unsigned long autosize;
+    int order, ngens;
+    const char *gens;
+};
+struct groups {
+    int ngroups;
+    const struct group *groups;
+};
+
+static const struct group groupdata[] = {
+    /* order 2 */
+    {1L, 2, 1, "BA"},
+    /* order 3 */
+    {2L, 3, 1, "BCA"},
+    /* order 4 */
+    {2L, 4, 1, "BCDA"},
+    {6L, 4, 2, "BADC" "CDAB"},
+    /* order 5 */
+    {4L, 5, 1, "BCDEA"},
+    /* order 6 */
+    {6L, 6, 2, "CFEBAD" "BADCFE"},
+    {2L, 6, 1, "DCFEBA"},
+    /* order 7 */
+    {6L, 7, 1, "BCDEFGA"},
+    /* order 8 */
+    {4L, 8, 1, "BCEFDGHA"},
+    {8L, 8, 2, "BDEFGAHC" "EGBHDCFA"},
+    {8L, 8, 2, "EGBHDCFA" "BAEFCDHG"},
+    {24L, 8, 2, "BDEFGAHC" "CHDGBEAF"},
+    {168L, 8, 3, "BAEFCDHG" "CEAGBHDF" "DFGAHBCE"},
+    /* order 9 */
+    {6L, 9, 1, "BDECGHFIA"},
+    {48L, 9, 2, "BDEAGHCIF" "CEFGHAIBD"},
+    /* order 10 */
+    {20L, 10, 2, "CJEBGDIFAH" "BADCFEHGJI"},
+    {4L, 10, 1, "DCFEHGJIBA"},
+    /* order 11 */
+    {10L, 11, 1, "BCDEFGHIJKA"},
+    /* order 12 */
+    {12L, 12, 2, "GLDKJEHCBIAF" "BCEFAGIJDKLH"},
+    {4L, 12, 1, "EHIJKCBLDGFA"},
+    {24L, 12, 2, "BEFGAIJKCDLH" "FJBKHLEGDCIA"},
+    {12L, 12, 2, "GLDKJEHCBIAF" "BAEFCDIJGHLK"},
+    {12L, 12, 2, "FDIJGHLBKAEC" "GIDKFLHCJEAB"},
+    /* order 13 */
+    {12L, 13, 1, "BCDEFGHIJKLMA"},
+    /* order 14 */
+    {42L, 14, 2, "ELGNIBKDMFAHCJ" "BADCFEHGJILKNM"},
+    {6L, 14, 1, "FEHGJILKNMBADC"},
+    /* order 15 */
+    {8L, 15, 1, "EGHCJKFMNIOBLDA"},
+    /* order 16 */
+    {8L, 16, 1, "MKNPFOADBGLCIEHJ"},
+    {96L, 16, 2, "ILKCONFPEDJHGMAB" "BDFGHIAKLMNCOEPJ"},
+    {32L, 16, 2, "MIHPFDCONBLAKJGE" "BEFGHJKALMNOCDPI"},
+    {32L, 16, 2, "IFACOGLMDEJBNPKH" "BEFGHJKALMNOCDPI"},
+    {16L, 16, 2, "MOHPFKCINBLADJGE" "BDFGHIEKLMNJOAPC"},
+    {16L, 16, 2, "MIHPFDJONBLEKCGA" "BDFGHIEKLMNJOAPC"},
+    {32L, 16, 2, "MOHPFDCINBLEKJGA" "BAFGHCDELMNIJKPO"},
+    {16L, 16, 2, "MIHPFKJONBLADCGE" "GDPHNOEKFLBCIAMJ"},
+    {32L, 16, 2, "MIBPFDJOGHLEKCNA" "CLEIJGMPKAOHNFDB"},
+    {192L, 16, 3,
+     "MCHPFAIJNBLDEOGK" "BEFGHJKALMNOCDPI" "GKLBNOEDFPHJIAMC"},
+    {64L, 16, 3, "MCHPFAIJNBLDEOGK" "LOGFPKJIBNMEDCHA" "CMAIJHPFDEONBLKG"},
+    {192L, 16, 3,
+     "IPKCOGMLEDJBNFAH" "BEFGHJKALMNOCDPI" "CMEIJBPFKAOGHLDN"},
+    {48L, 16, 3, "IPDJONFLEKCBGMAH" "FJBLMEOCGHPKAIND" "DGIEKLHNJOAMPBCF"},
+    {20160L, 16, 4,
+     "EHJKAMNBOCDPFGIL" "BAFGHCDELMNIJKPO" "CFAIJBLMDEOGHPKN"
+     "DGIAKLBNCOEFPHJM"},
+    /* order 17 */
+    {16L, 17, 1, "EFGHIJKLMNOPQABCD"},
+    /* order 18 */
+    {54L, 18, 2, "MKIQOPNAGLRECDBJHF" "BAEFCDJKLGHIOPMNRQ"},
+    {6L, 18, 1, "ECJKGHFOPDMNLRIQBA"},
+    {12L, 18, 2, "ECJKGHBOPAMNFRDQLI" "KNOPQCFREIGHLJAMBD"},
+    {432L, 18, 3,
+     "IFNAKLQCDOPBGHREMJ" "NOQCFRIGHKLJAMPBDE" "BAEFCDJKLGHIOPMNRQ"},
+    {48L, 18, 2, "ECJKGHBOPAMNFRDQLI" "FDKLHIOPBMNAREQCJG"},
+    /* order 19 */
+    {18L, 19, 1, "EFGHIJKLMNOPQRSABCD"},
+    /* order 20 */
+    {40L, 20, 2, "GTDKREHOBILSFMPCJQAN" "EABICDFMGHJQKLNTOPRS"},
+    {8L, 20, 1, "EHIJLCMNPGQRSKBTDOFA"},
+    {20L, 20, 2, "DJSHQNCLTRGPEBKAIFOM" "EABICDFMGHJQKLNTOPRS"},
+    {40L, 20, 2, "GTDKREHOBILSFMPCJQAN" "ECBIAGFMDKJQHONTLSRP"},
+    {24L, 20, 2, "IGFMDKJQHONTLSREPCBA" "FDIJGHMNKLQROPTBSAEC"},
+    /* order 21 */
+    {42L, 21, 2, "ITLSBOUERDHAGKCJNFMQP" "EJHLMKOPNRSQAUTCDBFGI"},
+    {12L, 21, 1, "EGHCJKFMNIPQLSTOUBRDA"},
+    /* order 22 */
+    {110L, 22, 2, "ETGVIBKDMFOHQJSLUNAPCR" "BADCFEHGJILKNMPORQTSVU"},
+    {10L, 22, 1, "FEHGJILKNMPORQTSVUBADC"},
+    /* order 23 */
+    {22L, 23, 1, "EFGHIJKLMNOPQRSTUVWABCD"},
+    /* order 24 */
+    {24L, 24, 2, "QXEJWPUMKLRIVBFTSACGHNDO" "HRNOPSWCTUVBLDIJXFGAKQME"},
+    {8L, 24, 1, "MQBTUDRWFGHXJELINOPKSAVC"},
+    {24L, 24, 2, "IOQRBEUVFWGHKLAXMNPSCDTJ" "NJXOVGDKSMTFIPQELCURBWAH"},
+    {48L, 24, 2, "QUEJWVXFKLRIPGMNSACBOTDH" "HSNOPWLDTUVBRIAKXFGCQEMJ"},
+    {24L, 24, 2, "QXEJWPUMKLRIVBFTSACGHNDO" "TWHNXLRIOPUMSACQVBFDEJGK"},
+    {48L, 24, 2, "QUEJWVXFKLRIPGMNSACBOTDH" "BAFGHCDEMNOPIJKLTUVQRSXW"},
+    {48L, 24, 3,
+     "QXKJWVUMESRIPGFTLDCBONAH" "JUEQRPXFKLWCVBMNSAIGHTDO"
+     "HSNOPWLDTUVBRIAKXFGCQEMJ"},
+    {24L, 24, 3,
+     "QUKJWPXFESRIVBMNLDCGHTAO" "JXEQRVUMKLWCPGFTSAIBONDH"
+     "TRONXLWCHVUMSAIJPGFDEQBK"},
+    {16L, 24, 2, "MRGTULWIOPFXSDJQBVNEKCHA" "VKXHOQASNTPBCWDEUFGIJLMR"},
+    {16L, 24, 2, "MRGTULWIOPFXSDJQBVNEKCHA" "RMLWIGTUSDJQOPFXEKCBVNAH"},
+    {48L, 24, 2, "IULQRGXMSDCWOPNTEKJBVFAH" "GLMOPRSDTUBVWIEKFXHJQANC"},
+    {24L, 24, 2, "UJPXMRCSNHGTLWIKFVBEDQOA" "NRUFVLWIPXMOJEDQHGTCSABK"},
+    {24L, 24, 2, "MIBTUAQRFGHXCDEWNOPJKLVS" "OKXVFWSCGUTNDRQJBPMALIHE"},
+    {144L, 24, 3,
+     "QXKJWVUMESRIPGFTLDCBONAH" "JUEQRPXFKLWCVBMNSAIGHTDO"
+     "BAFGHCDEMNOPIJKLTUVQRSXW"},
+    {336L, 24, 3,
+     "QTKJWONXESRIHVUMLDCPGFAB" "JNEQRHTUKLWCOPXFSAIVBMDG"
+     "HENOPJKLTUVBQRSAXFGWCDMI"},
+    /* order 25 */
+    {20L, 25, 1, "EHILMNPQRSFTUVBJWXDOYGAKC"},
+    {480L, 25, 2, "EHILMNPQRSCTUVBFWXDJYGOKA" "BDEGHIKLMNAPQRSCTUVFWXJYO"},
+    /* order 26 */
+    {156L, 26, 2,
+     "EXGZIBKDMFOHQJSLUNWPYRATCV" "BADCFEHGJILKNMPORQTSVUXWZY"},
+    {12L, 26, 1, "FEHGJILKNMPORQTSVUXWZYBADC"},
+};
+
+static const struct groups groups[] = {
+    {0, NULL},                  /* trivial case: 0 */
+    {0, NULL},                  /* trivial case: 1 */
+    {1, groupdata + 0},         /* 2 */
+    {1, groupdata + 1},         /* 3 */
+    {2, groupdata + 2},         /* 4 */
+    {1, groupdata + 4},         /* 5 */
+    {2, groupdata + 5},         /* 6 */
+    {1, groupdata + 7},         /* 7 */
+    {5, groupdata + 8},         /* 8 */
+    {2, groupdata + 13},        /* 9 */
+    {2, groupdata + 15},        /* 10 */
+    {1, groupdata + 17},        /* 11 */
+    {5, groupdata + 18},        /* 12 */
+    {1, groupdata + 23},        /* 13 */
+    {2, groupdata + 24},        /* 14 */
+    {1, groupdata + 26},        /* 15 */
+    {14, groupdata + 27},       /* 16 */
+    {1, groupdata + 41},        /* 17 */
+    {5, groupdata + 42},        /* 18 */
+    {1, groupdata + 47},        /* 19 */
+    {5, groupdata + 48},        /* 20 */
+    {2, groupdata + 53},        /* 21 */
+    {2, groupdata + 55},        /* 22 */
+    {1, groupdata + 57},        /* 23 */
+    {15, groupdata + 58},       /* 24 */
+    {2, groupdata + 73},        /* 25 */
+    {2, groupdata + 75},        /* 26 */
+};
+
+/* ----- data generated by group.gap ends ----- */
+
+static char *new_game_desc(const game_params *params, random_state *rs,
+			   char **aux, int interactive)
+{
+    int w = params->w, a = w*w;
+    digit *grid, *soln, *soln2;
+    int *indices;
+    int i, j, k, qh, qt;
+    int diff = params->diff;
+    const struct group *group;
+    char *desc, *p;
+
+    /*
+     * Difficulty exceptions: some combinations of size and
+     * difficulty cannot be satisfied, because all puzzles of at
+     * most that difficulty are actually even easier.
+     *
+     * Remember to re-test this whenever a change is made to the
+     * solver logic!
+     *
+     * I tested it using the following shell command:
+
+for d in t n h x u; do
+  for id in '' i; do
+    for i in {3..9}; do
+      echo -n "./group --generate 1 ${i}d${d}${id}: "
+      perl -e 'alarm 30; exec @ARGV' \
+        ./group --generate 1 ${i}d${d}${id} >/dev/null && echo ok
+    done
+  done
+done
+
+     * Of course, it's better to do that after taking the exceptions
+     * _out_, so as to detect exceptions that should be removed as
+     * well as those which should be added.
+     */
+    if (w < 5 && diff == DIFF_UNREASONABLE)
+	diff--;
+    if ((w < 5 || ((w == 6 || w == 8) && params->id)) && diff == DIFF_EXTREME)
+	diff--;
+    if ((w < 6 || (w == 6 && params->id)) && diff == DIFF_HARD)
+	diff--;
+    if ((w < 4 || (w == 4 && params->id)) && diff == DIFF_NORMAL)
+	diff--;
+
+    grid = snewn(a, digit);
+    soln = snewn(a, digit);
+    soln2 = snewn(a, digit);
+    indices = snewn(a, int);
+
+    while (1) {
+	/*
+	 * Construct a valid group table, by picking a group from
+	 * the above data table, decompressing it into a full
+	 * representation by BFS, and then randomly permuting its
+	 * non-identity elements.
+	 *
+	 * We build the canonical table in 'soln' (and use 'grid' as
+	 * our BFS queue), then transfer the table into 'grid'
+	 * having shuffled the rows.
+	 */
+	assert(w >= 2);
+	assert(w < lenof(groups));
+	group = groups[w].groups + random_upto(rs, groups[w].ngroups);
+	assert(group->order == w);
+	memset(soln, 0, a);
+	for (i = 0; i < w; i++)
+	    soln[i] = i+1;
+	qh = qt = 0;
+	grid[qt++] = 1;
+	while (qh < qt) {
+	    digit *row, *newrow;
+
+	    i = grid[qh++];
+	    row = soln + (i-1)*w;
+
+	    for (j = 0; j < group->ngens; j++) {
+		int nri;
+		const char *gen = group->gens + j*w;
+
+		/*
+		 * Apply each group generator to row, constructing a
+		 * new row.
+		 */
+		nri = gen[row[0]-1] - 'A' + 1;   /* which row is it? */
+		newrow = soln + (nri-1)*w;
+		if (!newrow[0]) {   /* not done yet */
+		    for (k = 0; k < w; k++)
+			newrow[k] = gen[row[k]-1] - 'A' + 1;
+		    grid[qt++] = nri;
+		}
+	    }
+	}
+	/* That's got the canonical table. Now shuffle it. */
+	for (i = 0; i < w; i++)
+	    soln2[i] = i;
+	if (params->id)		       /* do we shuffle in the identity? */
+	    shuffle(soln2+1, w-1, sizeof(*soln2), rs);
+	else
+	    shuffle(soln2, w, sizeof(*soln2), rs);
+	for (i = 0; i < w; i++)
+	    for (j = 0; j < w; j++)
+		grid[(soln2[i])*w+(soln2[j])] = soln2[soln[i*w+j]-1]+1;
+
+	/*
+	 * Remove entries one by one while the puzzle is still
+	 * soluble at the appropriate difficulty level.
+	 */
+	memcpy(soln, grid, a);
+	if (!params->id) {
+	    /*
+	     * Start by blanking the entire identity row and column,
+	     * and also another row and column so that the player
+	     * can't trivially determine which element is the
+	     * identity.
+	     */
+
+	    j = 1 + random_upto(rs, w-1);  /* pick a second row/col to blank */
+	    for (i = 0; i < w; i++) {
+		grid[(soln2[0])*w+i] = grid[i*w+(soln2[0])] = 0;
+		grid[(soln2[j])*w+i] = grid[i*w+(soln2[j])] = 0;
+	    }
+
+	    memcpy(soln2, grid, a);
+	    if (solver(params, soln2, diff) > diff)
+		continue;	       /* go round again if that didn't work */
+	}
+
+	k = 0;
+	for (i = (params->id ? 1 : 0); i < w; i++)
+	    for (j = (params->id ? 1 : 0); j < w; j++)
+		if (grid[i*w+j])
+		    indices[k++] = i*w+j;
+	shuffle(indices, k, sizeof(*indices), rs);
+
+	for (i = 0; i < k; i++) {
+	    memcpy(soln2, grid, a);
+	    soln2[indices[i]] = 0;
+	    if (solver(params, soln2, diff) <= diff)
+		grid[indices[i]] = 0;
+	}
+
+	/*
+	 * Make sure the puzzle isn't too easy.
+	 */
+	if (diff > 0) {
+	    memcpy(soln2, grid, a);
+	    if (solver(params, soln2, diff-1) < diff)
+		continue;	       /* go round and try again */
+	}
+
+	/*
+	 * Done.
+	 */
+	break;
+    }
+
+    /*
+     * Encode the puzzle description.
+     */
+    desc = snewn(a*20, char);
+    p = encode_grid(desc, grid, a);
+    *p++ = '\0';
+    desc = sresize(desc, p - desc, char);
+
+    /*
+     * Encode the solution.
+     */
+    *aux = snewn(a+2, char);
+    (*aux)[0] = 'S';
+    for (i = 0; i < a; i++)
+	(*aux)[i+1] = TOCHAR(soln[i], params->id);
+    (*aux)[a+1] = '\0';
+
+    sfree(grid);
+    sfree(soln);
+    sfree(soln2);
+    sfree(indices);
+
+    return desc;
+}
+
+/* ----------------------------------------------------------------------
+ * Gameplay.
+ */
+
+static char *validate_grid_desc(const char **pdesc, int range, int area)
+{
+    const char *desc = *pdesc;
+    int squares = 0;
+    while (*desc && *desc != ',') {
+        int n = *desc++;
+        if (n >= 'a' && n <= 'z') {
+            squares += n - 'a' + 1;
+        } else if (n == '_') {
+            /* do nothing */;
+        } else if (n > '0' && n <= '9') {
+            int val = atoi(desc-1);
+            if (val < 1 || val > range)
+                return "Out-of-range number in game description";
+            squares++;
+            while (*desc >= '0' && *desc <= '9')
+                desc++;
+        } else
+            return "Invalid character in game description";
+    }
+
+    if (squares < area)
+        return "Not enough data to fill grid";
+
+    if (squares > area)
+        return "Too much data to fit in grid";
+    *pdesc = desc;
+    return NULL;
+}
+
+static char *validate_desc(const game_params *params, const char *desc)
+{
+    int w = params->w, a = w*w;
+    const char *p = desc;
+
+    return validate_grid_desc(&p, w, a);
+}
+
+static const char *spec_to_grid(const char *desc, digit *grid, int area)
+{
+    int i = 0;
+    while (*desc && *desc != ',') {
+        int n = *desc++;
+        if (n >= 'a' && n <= 'z') {
+            int run = n - 'a' + 1;
+            assert(i + run <= area);
+            while (run-- > 0)
+                grid[i++] = 0;
+        } else if (n == '_') {
+            /* do nothing */;
+        } else if (n > '0' && n <= '9') {
+            assert(i < area);
+            grid[i++] = atoi(desc-1);
+            while (*desc >= '0' && *desc <= '9')
+                desc++;
+        } else {
+            assert(!"We can't get here");
+        }
+    }
+    assert(i == area);
+    return desc;
+}
+
+static game_state *new_game(midend *me, const game_params *params,
+                            const char *desc)
+{
+    int w = params->w, a = w*w;
+    game_state *state = snew(game_state);
+    int i;
+
+    state->par = *params;	       /* structure copy */
+    state->grid = snewn(a, digit);
+    state->immutable = snewn(a, unsigned char);
+    state->pencil = snewn(a, int);
+    for (i = 0; i < a; i++) {
+	state->grid[i] = 0;
+	state->immutable[i] = 0;
+	state->pencil[i] = 0;
+    }
+    state->sequence = snewn(w, digit);
+    state->dividers = snewn(w, int);
+    for (i = 0; i < w; i++) {
+	state->sequence[i] = i;
+	state->dividers[i] = -1;
+    }
+
+    desc = spec_to_grid(desc, state->grid, a);
+    for (i = 0; i < a; i++)
+	if (state->grid[i] != 0)
+	    state->immutable[i] = TRUE;
+
+    state->completed = state->cheated = FALSE;
+
+    return state;
+}
+
+static game_state *dup_game(const game_state *state)
+{
+    int w = state->par.w, a = w*w;
+    game_state *ret = snew(game_state);
+
+    ret->par = state->par;	       /* structure copy */
+
+    ret->grid = snewn(a, digit);
+    ret->immutable = snewn(a, unsigned char);
+    ret->pencil = snewn(a, int);
+    ret->sequence = snewn(w, digit);
+    ret->dividers = snewn(w, int);
+    memcpy(ret->grid, state->grid, a*sizeof(digit));
+    memcpy(ret->immutable, state->immutable, a*sizeof(unsigned char));
+    memcpy(ret->pencil, state->pencil, a*sizeof(int));
+    memcpy(ret->sequence, state->sequence, w*sizeof(digit));
+    memcpy(ret->dividers, state->dividers, w*sizeof(int));
+
+    ret->completed = state->completed;
+    ret->cheated = state->cheated;
+
+    return ret;
+}
+
+static void free_game(game_state *state)
+{
+    sfree(state->grid);
+    sfree(state->immutable);
+    sfree(state->pencil);
+    sfree(state->sequence);
+    sfree(state);
+}
+
+static char *solve_game(const game_state *state, const game_state *currstate,
+                        const char *aux, char **error)
+{
+    int w = state->par.w, a = w*w;
+    int i, ret;
+    digit *soln;
+    char *out;
+
+    if (aux)
+	return dupstr(aux);
+
+    soln = snewn(a, digit);
+    memcpy(soln, state->grid, a*sizeof(digit));
+
+    ret = solver(&state->par, soln, DIFFCOUNT-1);
+
+    if (ret == diff_impossible) {
+	*error = "No solution exists for this puzzle";
+	out = NULL;
+    } else if (ret == diff_ambiguous) {
+	*error = "Multiple solutions exist for this puzzle";
+	out = NULL;
+    } else {
+	out = snewn(a+2, char);
+	out[0] = 'S';
+	for (i = 0; i < a; i++)
+	    out[i+1] = TOCHAR(soln[i], state->par.id);
+	out[a+1] = '\0';
+    }
+
+    sfree(soln);
+    return out;
+}
+
+static int game_can_format_as_text_now(const game_params *params)
+{
+    return TRUE;
+}
+
+static char *game_text_format(const game_state *state)
+{
+    int w = state->par.w;
+    int x, y;
+    char *ret, *p, ch;
+
+    ret = snewn(2*w*w+1, char);	       /* leave room for terminating NUL */
+
+    p = ret;
+    for (y = 0; y < w; y++) {
+	for (x = 0; x < w; x++) {
+	    digit d = state->grid[y*w+x];
+
+            if (d == 0) {
+		ch = '.';
+	    } else {
+		ch = TOCHAR(d, state->par.id);
+	    }
+
+	    *p++ = ch;
+	    if (x == w-1) {
+		*p++ = '\n';
+	    } else {
+		*p++ = ' ';
+	    }
+	}
+    }
+
+    assert(p - ret == 2*w*w);
+    *p = '\0';
+    return ret;
+}
+
+struct game_ui {
+    /*
+     * These are the coordinates of the primary highlighted square on
+     * the grid, if hshow = 1.
+     */
+    int hx, hy;
+    /*
+     * These are the coordinates hx,hy _before_ they go through
+     * state->sequence.
+     */
+    int ohx, ohy;
+    /*
+     * These variables give the length and displacement of a diagonal
+     * sequence of highlighted squares starting at ohx,ohy (still if
+     * hshow = 1). To find the squares' real coordinates, for 0<=i<dn,
+     * compute ohx+i*odx and ohy+i*ody and then map through
+     * state->sequence.
+     */
+    int odx, ody, odn;
+    /*
+     * This indicates whether the current highlight is a
+     * pencil-mark one or a real one.
+     */
+    int hpencil;
+    /*
+     * This indicates whether or not we're showing the highlight
+     * (used to be hx = hy = -1); important so that when we're
+     * using the cursor keys it doesn't keep coming back at a
+     * fixed position. When hshow = 1, pressing a valid number
+     * or letter key or Space will enter that number or letter in the grid.
+     */
+    int hshow;
+    /*
+     * This indicates whether we're using the highlight as a cursor;
+     * it means that it doesn't vanish on a keypress, and that it is
+     * allowed on immutable squares.
+     */
+    int hcursor;
+    /*
+     * This indicates whether we're dragging a table header to
+     * reposition an entire row or column.
+     */
+    int drag;                          /* 0=none 1=row 2=col */
+    int dragnum;                       /* element being dragged */
+    int dragpos;                       /* its current position */
+    int edgepos;
+};
+
+static game_ui *new_ui(const game_state *state)
+{
+    game_ui *ui = snew(game_ui);
+
+    ui->hx = ui->hy = 0;
+    ui->hpencil = ui->hshow = ui->hcursor = 0;
+    ui->drag = 0;
+
+    return ui;
+}
+
+static void free_ui(game_ui *ui)
+{
+    sfree(ui);
+}
+
+static char *encode_ui(const game_ui *ui)
+{
+    return NULL;
+}
+
+static void decode_ui(game_ui *ui, const char *encoding)
+{
+}
+
+static void game_changed_state(game_ui *ui, const game_state *oldstate,
+                               const game_state *newstate)
+{
+    int w = newstate->par.w;
+    /*
+     * We prevent pencil-mode highlighting of a filled square, unless
+     * we're using the cursor keys. So if the user has just filled in
+     * a square which we had a pencil-mode highlight in (by Undo, or
+     * by Redo, or by Solve), then we cancel the highlight.
+     */
+    if (ui->hshow && ui->hpencil && !ui->hcursor &&
+        newstate->grid[ui->hy * w + ui->hx] != 0) {
+        ui->hshow = 0;
+    }
+    if (ui->hshow && ui->odn > 1) {
+        /*
+         * Reordering of rows or columns within the range of a
+         * multifill selection cancels the multifill and deselects
+         * everything.
+         */
+        int i;
+        for (i = 0; i < ui->odn; i++) {
+            if (oldstate->sequence[ui->ohx + i*ui->odx] !=
+                newstate->sequence[ui->ohx + i*ui->odx]) {
+                ui->hshow = 0;
+                break;
+            }
+            if (oldstate->sequence[ui->ohy + i*ui->ody] !=
+                newstate->sequence[ui->ohy + i*ui->ody]) {
+                ui->hshow = 0;
+                break;
+            }
+        }
+    } else if (ui->hshow &&
+               (newstate->sequence[ui->ohx] != ui->hx ||
+                newstate->sequence[ui->ohy] != ui->hy)) {
+        /*
+         * Otherwise, reordering of the row or column containing the
+         * selection causes the selection to move with it.
+         */
+        int i;
+        for (i = 0; i < w; i++) {
+            if (newstate->sequence[i] == ui->hx)
+                ui->ohx = i;
+            if (newstate->sequence[i] == ui->hy)
+                ui->ohy = i;
+        }
+    }
+}
+
+#define PREFERRED_TILESIZE 48
+#define TILESIZE (ds->tilesize)
+#define BORDER (TILESIZE / 2)
+#define LEGEND (TILESIZE)
+#define GRIDEXTRA max((TILESIZE / 32),1)
+#define COORD(x) ((x)*TILESIZE + BORDER + LEGEND)
+#define FROMCOORD(x) (((x)+(TILESIZE-BORDER-LEGEND)) / TILESIZE - 1)
+
+#define FLASH_TIME 0.4F
+
+#define DF_DIVIDER_TOP 0x1000
+#define DF_DIVIDER_BOT 0x2000
+#define DF_DIVIDER_LEFT 0x4000
+#define DF_DIVIDER_RIGHT 0x8000
+#define DF_HIGHLIGHT 0x0400
+#define DF_HIGHLIGHT_PENCIL 0x0200
+#define DF_IMMUTABLE 0x0100
+#define DF_LEGEND 0x0080
+#define DF_DIGIT_MASK 0x001F
+
+#define EF_DIGIT_SHIFT 5
+#define EF_DIGIT_MASK ((1 << EF_DIGIT_SHIFT) - 1)
+#define EF_LEFT_SHIFT 0
+#define EF_RIGHT_SHIFT (3*EF_DIGIT_SHIFT)
+#define EF_LEFT_MASK ((1UL << (3*EF_DIGIT_SHIFT)) - 1UL)
+#define EF_RIGHT_MASK (EF_LEFT_MASK << EF_RIGHT_SHIFT)
+#define EF_LATIN (1UL << (6*EF_DIGIT_SHIFT))
+
+struct game_drawstate {
+    game_params par;
+    int w, tilesize;
+    int started;
+    long *tiles, *legend, *pencil, *errors;
+    long *errtmp;
+    digit *sequence;
+};
+
+static int check_errors(const game_state *state, long *errors)
+{
+    int w = state->par.w, a = w*w;
+    digit *grid = state->grid;
+    int i, j, k, x, y, errs = FALSE;
+
+    /*
+     * To verify that we have a valid group table, it suffices to
+     * test latin-square-hood and associativity only. All the other
+     * group axioms follow from those two.
+     *
+     * Proof:
+     *
+     * Associativity is given; closure is obvious from latin-
+     * square-hood. We need to show that an identity exists and that
+     * every element has an inverse.
+     *
+     * Identity: take any element a. There will be some element e
+     * such that ea=a (in a latin square, every element occurs in
+     * every row and column, so a must occur somewhere in the a
+     * column, say on row e). For any other element b, there must
+     * exist x such that ax=b (same argument from latin-square-hood
+     * again), and then associativity gives us eb = e(ax) = (ea)x =
+     * ax = b. Hence eb=b for all b, i.e. e is a left-identity. A
+     * similar argument tells us that there must be some f which is
+     * a right-identity, and then we show they are the same element
+     * by observing that ef must simultaneously equal e and equal f.
+     *
+     * Inverses: given any a, by the latin-square argument again,
+     * there must exist p and q such that pa=e and aq=e (i.e. left-
+     * and right-inverses). We can show these are equal by
+     * associativity: p = pe = p(aq) = (pa)q = eq = q. []
+     */
+
+    if (errors)
+	for (i = 0; i < a; i++)
+	    errors[i] = 0;
+
+    for (y = 0; y < w; y++) {
+	unsigned long mask = 0, errmask = 0;
+	for (x = 0; x < w; x++) {
+	    unsigned long bit = 1UL << grid[y*w+x];
+	    errmask |= (mask & bit);
+	    mask |= bit;
+	}
+
+	if (mask != (1 << (w+1)) - (1 << 1)) {
+	    errs = TRUE;
+	    errmask &= ~1UL;
+	    if (errors) {
+		for (x = 0; x < w; x++)
+		    if (errmask & (1UL << grid[y*w+x]))
+			errors[y*w+x] |= EF_LATIN;
+	    }
+	}
+    }
+
+    for (x = 0; x < w; x++) {
+	unsigned long mask = 0, errmask = 0;
+	for (y = 0; y < w; y++) {
+	    unsigned long bit = 1UL << grid[y*w+x];
+	    errmask |= (mask & bit);
+	    mask |= bit;
+	}
+
+	if (mask != (1 << (w+1)) - (1 << 1)) {
+	    errs = TRUE;
+	    errmask &= ~1UL;
+	    if (errors) {
+		for (y = 0; y < w; y++)
+		    if (errmask & (1UL << grid[y*w+x]))
+			errors[y*w+x] |= EF_LATIN;
+	    }
+	}
+    }
+
+    for (i = 1; i < w; i++)
+	for (j = 1; j < w; j++)
+	    for (k = 1; k < w; k++)
+		if (grid[i*w+j] && grid[j*w+k] &&
+		    grid[(grid[i*w+j]-1)*w+k] &&
+		    grid[i*w+(grid[j*w+k]-1)] &&
+		    grid[(grid[i*w+j]-1)*w+k] != grid[i*w+(grid[j*w+k]-1)]) {
+		    if (errors) {
+			int a = i+1, b = j+1, c = k+1;
+			int ab = grid[i*w+j], bc = grid[j*w+k];
+			int left = (ab-1)*w+(c-1), right = (a-1)*w+(bc-1);
+			/*
+			 * If the appropriate error slot is already
+			 * used for one of the squares, we don't
+			 * fill either of them.
+			 */
+			if (!(errors[left] & EF_LEFT_MASK) &&
+			    !(errors[right] & EF_RIGHT_MASK)) {
+			    long err;
+			    err = a;
+			    err = (err << EF_DIGIT_SHIFT) | b;
+			    err = (err << EF_DIGIT_SHIFT) | c;
+			    errors[left] |= err << EF_LEFT_SHIFT;
+			    errors[right] |= err << EF_RIGHT_SHIFT;
+			}
+		    }
+		    errs = TRUE;
+		}
+
+    return errs;
+}
+
+static int find_in_sequence(digit *seq, int len, digit n)
+{
+    int i;
+
+    for (i = 0; i < len; i++)
+        if (seq[i] == n)
+            return i;
+
+    assert(!"Should never get here");
+    return -1;
+}
+
+static char *interpret_move(const game_state *state, game_ui *ui,
+                            const game_drawstate *ds,
+                            int x, int y, int button)
+{
+    int w = state->par.w;
+    int tx, ty;
+    char buf[80];
+
+    button &= ~MOD_MASK;
+
+    tx = FROMCOORD(x);
+    ty = FROMCOORD(y);
+
+    if (ui->drag) {
+        if (IS_MOUSE_DRAG(button)) {
+            int tcoord = ((ui->drag &~ 4) == 1 ? ty : tx);
+            ui->drag |= 4;             /* some movement has happened */
+            if (tcoord >= 0 && tcoord < w) {
+                ui->dragpos = tcoord;
+                return "";
+            }
+        } else if (IS_MOUSE_RELEASE(button)) {
+            if (ui->drag & 4) {
+                ui->drag = 0;          /* end drag */
+                if (state->sequence[ui->dragpos] == ui->dragnum)
+                    return "";         /* drag was a no-op overall */
+                sprintf(buf, "D%d,%d", ui->dragnum, ui->dragpos);
+                return dupstr(buf);
+            } else {
+                ui->drag = 0;          /* end 'drag' */
+                if (ui->edgepos > 0 && ui->edgepos < w) {
+                    sprintf(buf, "V%d,%d",
+                            state->sequence[ui->edgepos-1],
+                            state->sequence[ui->edgepos]);
+                    return dupstr(buf);
+                } else
+                    return "";         /* no-op */
+            }
+        }
+    } else if (IS_MOUSE_DOWN(button)) {
+        if (tx >= 0 && tx < w && ty >= 0 && ty < w) {
+            int otx = tx, oty = ty;
+            tx = state->sequence[tx];
+            ty = state->sequence[ty];
+            if (button == LEFT_BUTTON) {
+                if (tx == ui->hx && ty == ui->hy &&
+                    ui->hshow && ui->hpencil == 0) {
+                    ui->hshow = 0;
+                } else {
+                    ui->hx = tx;
+                    ui->hy = ty;
+                    ui->ohx = otx;
+                    ui->ohy = oty;
+                    ui->odx = ui->ody = 0;
+                    ui->odn = 1;
+                    ui->hshow = !state->immutable[ty*w+tx];
+                    ui->hpencil = 0;
+                }
+                ui->hcursor = 0;
+                return "";		       /* UI activity occurred */
+            }
+            if (button == RIGHT_BUTTON) {
+                /*
+                 * Pencil-mode highlighting for non filled squares.
+                 */
+                if (state->grid[ty*w+tx] == 0) {
+                    if (tx == ui->hx && ty == ui->hy &&
+                        ui->hshow && ui->hpencil) {
+                        ui->hshow = 0;
+                    } else {
+                        ui->hpencil = 1;
+                        ui->hx = tx;
+                        ui->hy = ty;
+                        ui->ohx = otx;
+                        ui->ohy = oty;
+                        ui->odx = ui->ody = 0;
+                        ui->odn = 1;
+                        ui->hshow = 1;
+                    }
+                } else {
+                    ui->hshow = 0;
+                }
+                ui->hcursor = 0;
+                return "";		       /* UI activity occurred */
+            }
+        } else if (tx >= 0 && tx < w && ty == -1) {
+            ui->drag = 2;
+            ui->dragnum = state->sequence[tx];
+            ui->dragpos = tx;
+            ui->edgepos = FROMCOORD(x + TILESIZE/2);
+            return "";
+        } else if (ty >= 0 && ty < w && tx == -1) {
+            ui->drag = 1;
+            ui->dragnum = state->sequence[ty];
+            ui->dragpos = ty;
+            ui->edgepos = FROMCOORD(y + TILESIZE/2);
+            return "";
+        }
+    } else if (IS_MOUSE_DRAG(button)) {
+        if (!ui->hpencil &&
+            tx >= 0 && tx < w && ty >= 0 && ty < w &&
+            abs(tx - ui->ohx) == abs(ty - ui->ohy)) {
+            ui->odn = abs(tx - ui->ohx) + 1;
+            ui->odx = (tx < ui->ohx ? -1 : +1);
+            ui->ody = (ty < ui->ohy ? -1 : +1);
+        } else {
+            ui->odx = ui->ody = 0;
+            ui->odn = 1;
+        }
+        return "";
+    }
+
+    if (IS_CURSOR_MOVE(button)) {
+        int cx = find_in_sequence(state->sequence, w, ui->hx);
+        int cy = find_in_sequence(state->sequence, w, ui->hy);
+        move_cursor(button, &cx, &cy, w, w, 0);
+        ui->hx = state->sequence[cx];
+        ui->hy = state->sequence[cy];
+        ui->hshow = ui->hcursor = 1;
+        return "";
+    }
+    if (ui->hshow &&
+        (button == CURSOR_SELECT)) {
+        ui->hpencil = 1 - ui->hpencil;
+        ui->hcursor = 1;
+        return "";
+    }
+
+    if (ui->hshow &&
+	((ISCHAR(button) && FROMCHAR(button, state->par.id) <= w) ||
+	 button == CURSOR_SELECT2 || button == '\b')) {
+	int n = FROMCHAR(button, state->par.id);
+	int i, buflen;
+        char *movebuf;
+
+	if (button == CURSOR_SELECT2 || button == '\b')
+	    n = 0;
+
+        for (i = 0; i < ui->odn; i++) {
+            int x = state->sequence[ui->ohx + i*ui->odx];
+            int y = state->sequence[ui->ohy + i*ui->ody];
+            int index = y*w+x;
+
+            /*
+             * Can't make pencil marks in a filled square. This can only
+             * become highlighted if we're using cursor keys.
+             */
+            if (ui->hpencil && state->grid[index])
+                return NULL;
+
+            /*
+             * Can't do anything to an immutable square. Exception:
+             * trying to set it to what it already was is OK (so that
+             * multifilling can set a whole diagonal to a without
+             * having to detour round the one immutable square in the
+             * middle that already said a).
+             */
+            if (!ui->hpencil && state->grid[index] == n)
+                /* OK even if it is immutable */;
+            else if (state->immutable[index])
+                return NULL;
+        }
+
+        movebuf = snewn(80 * ui->odn, char);
+        buflen = sprintf(movebuf, "%c%d,%d,%d",
+                         (char)(ui->hpencil && n > 0 ? 'P' : 'R'),
+                         ui->hx, ui->hy, n);
+        for (i = 1; i < ui->odn; i++) {
+            assert(buflen < i*80);
+            buflen += sprintf(movebuf + buflen, "+%d,%d",
+                              state->sequence[ui->ohx + i*ui->odx],
+                              state->sequence[ui->ohy + i*ui->ody]);
+        }
+        movebuf = sresize(movebuf, buflen+1, char);
+
+        if (!ui->hcursor) ui->hshow = 0;
+
+	return movebuf;
+    }
+
+    if (button == 'M' || button == 'm')
+        return dupstr("M");
+
+    return NULL;
+}
+
+static game_state *execute_move(const game_state *from, const char *move)
+{
+    int w = from->par.w, a = w*w;
+    game_state *ret;
+    int x, y, i, j, n, pos;
+
+    if (move[0] == 'S') {
+	ret = dup_game(from);
+	ret->completed = ret->cheated = TRUE;
+
+	for (i = 0; i < a; i++) {
+	    if (!ISCHAR(move[i+1]) || FROMCHAR(move[i+1], from->par.id) > w) {
+		free_game(ret);
+		return NULL;
+	    }
+	    ret->grid[i] = FROMCHAR(move[i+1], from->par.id);
+	    ret->pencil[i] = 0;
+	}
+
+	if (move[a+1] != '\0') {
+	    free_game(ret);
+	    return NULL;
+	}
+
+	return ret;
+    } else if ((move[0] == 'P' || move[0] == 'R') &&
+               sscanf(move+1, "%d,%d,%d%n", &x, &y, &n, &pos) == 3 &&
+               n >= 0 && n <= w) {
+        const char *mp = move + 1 + pos;
+        int pencil = (move[0] == 'P');
+        ret = dup_game(from);
+
+        while (1) {
+            if (x < 0 || x >= w || y < 0 || y >= w) {
+                free_game(ret);
+                return NULL;
+            }
+            if (from->immutable[y*w+x] && !(!pencil && from->grid[y*w+x] == n))
+                return NULL;
+
+            if (move[0] == 'P' && n > 0) {
+                ret->pencil[y*w+x] ^= 1 << n;
+            } else {
+                ret->grid[y*w+x] = n;
+                ret->pencil[y*w+x] = 0;
+            }
+
+            if (!*mp)
+                break;
+
+            if (*mp != '+')
+                return NULL;
+            if (sscanf(mp, "+%d,%d%n", &x, &y, &pos) < 2)
+                return NULL;
+            mp += pos;
+        }
+
+        if (!ret->completed && !check_errors(ret, NULL))
+            ret->completed = TRUE;
+
+	return ret;
+    } else if (move[0] == 'M') {
+	/*
+	 * Fill in absolutely all pencil marks everywhere. (I
+	 * wouldn't use this for actual play, but it's a handy
+	 * starting point when following through a set of
+	 * diagnostics output by the standalone solver.)
+	 */
+	ret = dup_game(from);
+	for (i = 0; i < a; i++) {
+	    if (!ret->grid[i])
+		ret->pencil[i] = (1 << (w+1)) - (1 << 1);
+	}
+	return ret;
+    } else if (move[0] == 'D' &&
+               sscanf(move+1, "%d,%d", &x, &y) == 2) {
+	/*
+	 * Reorder the rows and columns so that digit x is in position
+	 * y.
+	 */
+	ret = dup_game(from);
+	for (i = j = 0; i < w; i++) {
+            if (i == y) {
+                ret->sequence[i] = x;
+            } else {
+                if (from->sequence[j] == x)
+                    j++;
+                ret->sequence[i] = from->sequence[j++];
+            }
+	}
+        /*
+         * Eliminate any obsoleted dividers.
+         */
+        for (x = 0; x < w; x++) {
+            int i = ret->sequence[x];
+            int j = (x+1 < w ? ret->sequence[x+1] : -1);
+            if (ret->dividers[i] != j)
+                ret->dividers[i] = -1;
+        }
+	return ret;
+    } else if (move[0] == 'V' &&
+               sscanf(move+1, "%d,%d", &i, &j) == 2) {
+	ret = dup_game(from);
+        if (ret->dividers[i] == j)
+            ret->dividers[i] = -1;
+        else
+            ret->dividers[i] = j;
+	return ret;
+    } else
+	return NULL;		       /* couldn't parse move string */
+}
+
+/* ----------------------------------------------------------------------
+ * Drawing routines.
+ */
+
+#define SIZE(w) ((w) * TILESIZE + 2*BORDER + LEGEND)
+
+static void game_compute_size(const game_params *params, int tilesize,
+                              int *x, int *y)
+{
+    /* Ick: fake up `ds->tilesize' for macro expansion purposes */
+    struct { int tilesize; } ads, *ds = &ads;
+    ads.tilesize = tilesize;
+
+    *x = *y = SIZE(params->w);
+}
+
+static void game_set_size(drawing *dr, game_drawstate *ds,
+                          const game_params *params, int tilesize)
+{
+    ds->tilesize = tilesize;
+}
+
+static float *game_colours(frontend *fe, int *ncolours)
+{
+    float *ret = snewn(3 * NCOLOURS, float);
+
+    frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
+
+    ret[COL_GRID * 3 + 0] = 0.0F;
+    ret[COL_GRID * 3 + 1] = 0.0F;
+    ret[COL_GRID * 3 + 2] = 0.0F;
+
+    ret[COL_USER * 3 + 0] = 0.0F;
+    ret[COL_USER * 3 + 1] = 0.6F * ret[COL_BACKGROUND * 3 + 1];
+    ret[COL_USER * 3 + 2] = 0.0F;
+
+    ret[COL_HIGHLIGHT * 3 + 0] = 0.78F * ret[COL_BACKGROUND * 3 + 0];
+    ret[COL_HIGHLIGHT * 3 + 1] = 0.78F * ret[COL_BACKGROUND * 3 + 1];
+    ret[COL_HIGHLIGHT * 3 + 2] = 0.78F * ret[COL_BACKGROUND * 3 + 2];
+
+    ret[COL_ERROR * 3 + 0] = 1.0F;
+    ret[COL_ERROR * 3 + 1] = 0.0F;
+    ret[COL_ERROR * 3 + 2] = 0.0F;
+
+    ret[COL_PENCIL * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
+    ret[COL_PENCIL * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
+    ret[COL_PENCIL * 3 + 2] = ret[COL_BACKGROUND * 3 + 2];
+
+    ret[COL_DIAGONAL * 3 + 0] = 0.95F * ret[COL_BACKGROUND * 3 + 0];
+    ret[COL_DIAGONAL * 3 + 1] = 0.95F * ret[COL_BACKGROUND * 3 + 1];
+    ret[COL_DIAGONAL * 3 + 2] = 0.95F * ret[COL_BACKGROUND * 3 + 2];
+
+    *ncolours = NCOLOURS;
+    return ret;
+}
+
+static game_drawstate *game_new_drawstate(drawing *dr, const game_state *state)
+{
+    int w = state->par.w, a = w*w;
+    struct game_drawstate *ds = snew(struct game_drawstate);
+    int i;
+
+    ds->w = w;
+    ds->par = state->par;	       /* structure copy */
+    ds->tilesize = 0;
+    ds->started = FALSE;
+    ds->tiles = snewn(a, long);
+    ds->legend = snewn(w, long);
+    ds->pencil = snewn(a, long);
+    ds->errors = snewn(a, long);
+    ds->sequence = snewn(a, digit);
+    for (i = 0; i < a; i++)
+	ds->tiles[i] = ds->pencil[i] = -1;
+    for (i = 0; i < w; i++)
+	ds->legend[i] = -1;
+    ds->errtmp = snewn(a, long);
+
+    return ds;
+}
+
+static void game_free_drawstate(drawing *dr, game_drawstate *ds)
+{
+    sfree(ds->tiles);
+    sfree(ds->pencil);
+    sfree(ds->errors);
+    sfree(ds->errtmp);
+    sfree(ds->sequence);
+    sfree(ds);
+}
+
+static void draw_tile(drawing *dr, game_drawstate *ds, int x, int y, long tile,
+		      long pencil, long error)
+{
+    int w = ds->w /* , a = w*w */;
+    int tx, ty, tw, th;
+    int cx, cy, cw, ch;
+    char str[64];
+
+    tx = BORDER + LEGEND + x * TILESIZE + 1;
+    ty = BORDER + LEGEND + y * TILESIZE + 1;
+
+    cx = tx;
+    cy = ty;
+    cw = tw = TILESIZE-1;
+    ch = th = TILESIZE-1;
+
+    if (tile & DF_LEGEND) {
+        cx += TILESIZE/10;
+        cy += TILESIZE/10;
+        cw -= TILESIZE/5;
+        ch -= TILESIZE/5;
+        tile |= DF_IMMUTABLE;
+    }
+
+    clip(dr, cx, cy, cw, ch);
+
+    /* background needs erasing */
+    draw_rect(dr, cx, cy, cw, ch,
+	      (tile & DF_HIGHLIGHT) ? COL_HIGHLIGHT :
+              (x == y) ? COL_DIAGONAL : COL_BACKGROUND);
+
+    /* dividers */
+    if (tile & DF_DIVIDER_TOP)
+        draw_rect(dr, cx, cy, cw, 1, COL_GRID);
+    if (tile & DF_DIVIDER_BOT)
+        draw_rect(dr, cx, cy+ch-1, cw, 1, COL_GRID);
+    if (tile & DF_DIVIDER_LEFT)
+        draw_rect(dr, cx, cy, 1, ch, COL_GRID);
+    if (tile & DF_DIVIDER_RIGHT)
+        draw_rect(dr, cx+cw-1, cy, 1, ch, COL_GRID);
+
+    /* pencil-mode highlight */
+    if (tile & DF_HIGHLIGHT_PENCIL) {
+        int coords[6];
+        coords[0] = cx;
+        coords[1] = cy;
+        coords[2] = cx+cw/2;
+        coords[3] = cy;
+        coords[4] = cx;
+        coords[5] = cy+ch/2;
+        draw_polygon(dr, coords, 3, COL_HIGHLIGHT, COL_HIGHLIGHT);
+    }
+
+    /* new number needs drawing? */
+    if (tile & DF_DIGIT_MASK) {
+	str[1] = '\0';
+	str[0] = TOCHAR(tile & DF_DIGIT_MASK, ds->par.id);
+	draw_text(dr, tx + TILESIZE/2, ty + TILESIZE/2,
+		  FONT_VARIABLE, TILESIZE/2, ALIGN_VCENTRE | ALIGN_HCENTRE,
+		  (error & EF_LATIN) ? COL_ERROR :
+		  (tile & DF_IMMUTABLE) ? COL_GRID : COL_USER, str);
+
+	if (error & EF_LEFT_MASK) {
+	    int a = (error >> (EF_LEFT_SHIFT+2*EF_DIGIT_SHIFT))&EF_DIGIT_MASK;
+	    int b = (error >> (EF_LEFT_SHIFT+1*EF_DIGIT_SHIFT))&EF_DIGIT_MASK;
+	    int c = (error >> (EF_LEFT_SHIFT                 ))&EF_DIGIT_MASK;
+	    char buf[10];
+	    sprintf(buf, "(%c%c)%c", TOCHAR(a, ds->par.id),
+		    TOCHAR(b, ds->par.id), TOCHAR(c, ds->par.id));
+	    draw_text(dr, tx + TILESIZE/2, ty + TILESIZE/6,
+		      FONT_VARIABLE, TILESIZE/6, ALIGN_VCENTRE | ALIGN_HCENTRE,
+		      COL_ERROR, buf);
+	}
+	if (error & EF_RIGHT_MASK) {
+	    int a = (error >> (EF_RIGHT_SHIFT+2*EF_DIGIT_SHIFT))&EF_DIGIT_MASK;
+	    int b = (error >> (EF_RIGHT_SHIFT+1*EF_DIGIT_SHIFT))&EF_DIGIT_MASK;
+	    int c = (error >> (EF_RIGHT_SHIFT                 ))&EF_DIGIT_MASK;
+	    char buf[10];
+	    sprintf(buf, "%c(%c%c)", TOCHAR(a, ds->par.id),
+		    TOCHAR(b, ds->par.id), TOCHAR(c, ds->par.id));
+	    draw_text(dr, tx + TILESIZE/2, ty + TILESIZE - TILESIZE/6,
+		      FONT_VARIABLE, TILESIZE/6, ALIGN_VCENTRE | ALIGN_HCENTRE,
+		      COL_ERROR, buf);
+	}
+    } else {
+        int i, j, npencil;
+	int pl, pr, pt, pb;
+	float bestsize;
+	int pw, ph, minph, pbest, fontsize;
+
+        /* Count the pencil marks required. */
+        for (i = 1, npencil = 0; i <= w; i++)
+            if (pencil & (1 << i))
+		npencil++;
+	if (npencil) {
+
+	    minph = 2;
+
+	    /*
+	     * Determine the bounding rectangle within which we're going
+	     * to put the pencil marks.
+	     */
+	    /* Start with the whole square */
+	    pl = tx + GRIDEXTRA;
+	    pr = pl + TILESIZE - GRIDEXTRA;
+	    pt = ty + GRIDEXTRA;
+	    pb = pt + TILESIZE - GRIDEXTRA;
+
+	    /*
+	     * We arrange our pencil marks in a grid layout, with
+	     * the number of rows and columns adjusted to allow the
+	     * maximum font size.
+	     *
+	     * So now we work out what the grid size ought to be.
+	     */
+	    bestsize = 0.0;
+	    pbest = 0;
+	    /* Minimum */
+	    for (pw = 3; pw < max(npencil,4); pw++) {
+		float fw, fh, fs;
+
+		ph = (npencil + pw - 1) / pw;
+		ph = max(ph, minph);
+		fw = (pr - pl) / (float)pw;
+		fh = (pb - pt) / (float)ph;
+		fs = min(fw, fh);
+		if (fs > bestsize) {
+		    bestsize = fs;
+		    pbest = pw;
+		}
+	    }
+	    assert(pbest > 0);
+	    pw = pbest;
+	    ph = (npencil + pw - 1) / pw;
+	    ph = max(ph, minph);
+
+	    /*
+	     * Now we've got our grid dimensions, work out the pixel
+	     * size of a grid element, and round it to the nearest
+	     * pixel. (We don't want rounding errors to make the
+	     * grid look uneven at low pixel sizes.)
+	     */
+	    fontsize = min((pr - pl) / pw, (pb - pt) / ph);
+
+	    /*
+	     * Centre the resulting figure in the square.
+	     */
+	    pl = tx + (TILESIZE - fontsize * pw) / 2;
+	    pt = ty + (TILESIZE - fontsize * ph) / 2;
+
+	    /*
+	     * Now actually draw the pencil marks.
+	     */
+	    for (i = 1, j = 0; i <= w; i++)
+		if (pencil & (1 << i)) {
+		    int dx = j % pw, dy = j / pw;
+
+		    str[1] = '\0';
+		    str[0] = TOCHAR(i, ds->par.id);
+		    draw_text(dr, pl + fontsize * (2*dx+1) / 2,
+			      pt + fontsize * (2*dy+1) / 2,
+			      FONT_VARIABLE, fontsize,
+			      ALIGN_VCENTRE | ALIGN_HCENTRE, COL_PENCIL, str);
+		    j++;
+		}
+	}
+    }
+
+    unclip(dr);
+
+    draw_update(dr, cx, cy, cw, ch);
+}
+
+static void game_redraw(drawing *dr, game_drawstate *ds,
+                        const game_state *oldstate, const game_state *state,
+                        int dir, const game_ui *ui,
+                        float animtime, float flashtime)
+{
+    int w = state->par.w /*, a = w*w */;
+    int x, y, i, j;
+
+    if (!ds->started) {
+	/*
+	 * The initial contents of the window are not guaranteed and
+	 * can vary with front ends. To be on the safe side, all
+	 * games should start by drawing a big background-colour
+	 * rectangle covering the whole window.
+	 */
+	draw_rect(dr, 0, 0, SIZE(w), SIZE(w), COL_BACKGROUND);
+
+	/*
+	 * Big containing rectangle.
+	 */
+	draw_rect(dr, COORD(0) - GRIDEXTRA, COORD(0) - GRIDEXTRA,
+		  w*TILESIZE+1+GRIDEXTRA*2, w*TILESIZE+1+GRIDEXTRA*2,
+		  COL_GRID);
+
+	draw_update(dr, 0, 0, SIZE(w), SIZE(w));
+
+	ds->started = TRUE;
+    }
+
+    check_errors(state, ds->errtmp);
+
+    /*
+     * Construct a modified version of state->sequence which takes
+     * into account an unfinished drag operation.
+     */
+    if (ui->drag) {
+        x = ui->dragnum;
+        y = ui->dragpos;
+    } else {
+        x = y = -1;
+    }
+    for (i = j = 0; i < w; i++) {
+        if (i == y) {
+            ds->sequence[i] = x;
+        } else {
+            if (state->sequence[j] == x)
+                j++;
+            ds->sequence[i] = state->sequence[j++];
+        }
+    }
+
+    /*
+     * Draw the table legend.
+     */
+    for (x = 0; x < w; x++) {
+        int sx = ds->sequence[x];
+        long tile = (sx+1) | DF_LEGEND;
+        if (ds->legend[x] != tile) {
+            ds->legend[x] = tile;
+            draw_tile(dr, ds, -1, x, tile, 0, 0);
+            draw_tile(dr, ds, x, -1, tile, 0, 0);
+        }
+    }
+
+    for (y = 0; y < w; y++) {
+        int sy = ds->sequence[y];
+	for (x = 0; x < w; x++) {
+	    long tile = 0L, pencil = 0L, error;
+            int sx = ds->sequence[x];
+
+	    if (state->grid[sy*w+sx])
+		tile = state->grid[sy*w+sx];
+	    else
+		pencil = (long)state->pencil[sy*w+sx];
+
+	    if (state->immutable[sy*w+sx])
+		tile |= DF_IMMUTABLE;
+
+            if ((ui->drag == 5 && ui->dragnum == sy) ||
+                (ui->drag == 6 && ui->dragnum == sx)) {
+                tile |= DF_HIGHLIGHT;
+            } else if (ui->hshow) {
+                int i = abs(x - ui->ohx);
+                int highlight = 0;
+                if (ui->odn > 1) {
+                    /*
+                     * When a diagonal multifill selection is shown,
+                     * we show it in its original grid position
+                     * regardless of in-progress row/col drags. Moving
+                     * every square about would be horrible.
+                     */
+                    if (i >= 0 && i < ui->odn &&
+                        x == ui->ohx + i*ui->odx &&
+                        y == ui->ohy + i*ui->ody)
+                        highlight = 1;
+                } else {
+                    /*
+                     * For a single square, we move its highlight
+                     * around with the drag.
+                     */
+                    highlight = (ui->hx == sx && ui->hy == sy);
+                }
+                if (highlight)
+                    tile |= (ui->hpencil ? DF_HIGHLIGHT_PENCIL : DF_HIGHLIGHT);
+            }
+
+            if (flashtime > 0 &&
+                (flashtime <= FLASH_TIME/3 ||
+                 flashtime >= FLASH_TIME*2/3))
+                tile |= DF_HIGHLIGHT;  /* completion flash */
+
+            if (y <= 0 || state->dividers[ds->sequence[y-1]] == sy)
+                tile |= DF_DIVIDER_TOP;
+            if (y+1 >= w || state->dividers[sy] == ds->sequence[y+1])
+                tile |= DF_DIVIDER_BOT;
+            if (x <= 0 || state->dividers[ds->sequence[x-1]] == sx)
+                tile |= DF_DIVIDER_LEFT;
+            if (x+1 >= w || state->dividers[sx] == ds->sequence[x+1])
+                tile |= DF_DIVIDER_RIGHT;
+
+	    error = ds->errtmp[sy*w+sx];
+
+	    if (ds->tiles[y*w+x] != tile ||
+		ds->pencil[y*w+x] != pencil ||
+		ds->errors[y*w+x] != error) {
+		ds->tiles[y*w+x] = tile;
+		ds->pencil[y*w+x] = pencil;
+		ds->errors[y*w+x] = error;
+		draw_tile(dr, ds, x, y, tile, pencil, error);
+	    }
+	}
+    }
+}
+
+static float game_anim_length(const game_state *oldstate,
+                              const game_state *newstate, int dir, game_ui *ui)
+{
+    return 0.0F;
+}
+
+static float game_flash_length(const game_state *oldstate,
+                               const game_state *newstate, int dir, game_ui *ui)
+{
+    if (!oldstate->completed && newstate->completed &&
+	!oldstate->cheated && !newstate->cheated)
+        return FLASH_TIME;
+    return 0.0F;
+}
+
+static int game_status(const game_state *state)
+{
+    return state->completed ? +1 : 0;
+}
+
+static int game_timing_state(const game_state *state, game_ui *ui)
+{
+    if (state->completed)
+	return FALSE;
+    return TRUE;
+}
+
+static void game_print_size(const game_params *params, float *x, float *y)
+{
+    int pw, ph;
+
+    /*
+     * We use 9mm squares by default, like Solo.
+     */
+    game_compute_size(params, 900, &pw, &ph);
+    *x = pw / 100.0F;
+    *y = ph / 100.0F;
+}
+
+static void game_print(drawing *dr, const game_state *state, int tilesize)
+{
+    int w = state->par.w;
+    int ink = print_mono_colour(dr, 0);
+    int x, y;
+
+    /* Ick: fake up `ds->tilesize' for macro expansion purposes */
+    game_drawstate ads, *ds = &ads;
+    game_set_size(dr, ds, NULL, tilesize);
+
+    /*
+     * Border.
+     */
+    print_line_width(dr, 3 * TILESIZE / 40);
+    draw_rect_outline(dr, BORDER + LEGEND, BORDER + LEGEND,
+		      w*TILESIZE, w*TILESIZE, ink);
+
+    /*
+     * Legend on table.
+     */
+    for (x = 0; x < w; x++) {
+	char str[2];
+	str[1] = '\0';
+	str[0] = TOCHAR(x+1, state->par.id);
+	draw_text(dr, BORDER+LEGEND + x*TILESIZE + TILESIZE/2,
+		  BORDER + TILESIZE/2,
+		  FONT_VARIABLE, TILESIZE/2,
+		  ALIGN_VCENTRE | ALIGN_HCENTRE, ink, str);
+	draw_text(dr, BORDER + TILESIZE/2,
+		  BORDER+LEGEND + x*TILESIZE + TILESIZE/2,
+		  FONT_VARIABLE, TILESIZE/2,
+		  ALIGN_VCENTRE | ALIGN_HCENTRE, ink, str);
+    }
+
+    /*
+     * Main grid.
+     */
+    for (x = 1; x < w; x++) {
+	print_line_width(dr, TILESIZE / 40);
+	draw_line(dr, BORDER+LEGEND+x*TILESIZE, BORDER+LEGEND,
+		  BORDER+LEGEND+x*TILESIZE, BORDER+LEGEND+w*TILESIZE, ink);
+    }
+    for (y = 1; y < w; y++) {
+	print_line_width(dr, TILESIZE / 40);
+	draw_line(dr, BORDER+LEGEND, BORDER+LEGEND+y*TILESIZE,
+		  BORDER+LEGEND+w*TILESIZE, BORDER+LEGEND+y*TILESIZE, ink);
+    }
+
+    /*
+     * Numbers.
+     */
+    for (y = 0; y < w; y++)
+	for (x = 0; x < w; x++)
+	    if (state->grid[y*w+x]) {
+		char str[2];
+		str[1] = '\0';
+		str[0] = TOCHAR(state->grid[y*w+x], state->par.id);
+		draw_text(dr, BORDER+LEGEND + x*TILESIZE + TILESIZE/2,
+			  BORDER+LEGEND + y*TILESIZE + TILESIZE/2,
+			  FONT_VARIABLE, TILESIZE/2,
+			  ALIGN_VCENTRE | ALIGN_HCENTRE, ink, str);
+	    }
+}
+
+#ifdef COMBINED
+#define thegame group
+#endif
+
+const struct game thegame = {
+    "Group", NULL, NULL,
+    default_params,
+    game_fetch_preset,
+    decode_params,
+    encode_params,
+    free_params,
+    dup_params,
+    TRUE, game_configure, custom_params,
+    validate_params,
+    new_game_desc,
+    validate_desc,
+    new_game,
+    dup_game,
+    free_game,
+    TRUE, solve_game,
+    TRUE, game_can_format_as_text_now, game_text_format,
+    new_ui,
+    free_ui,
+    encode_ui,
+    decode_ui,
+    game_changed_state,
+    interpret_move,
+    execute_move,
+    PREFERRED_TILESIZE, game_compute_size, game_set_size,
+    game_colours,
+    game_new_drawstate,
+    game_free_drawstate,
+    game_redraw,
+    game_anim_length,
+    game_flash_length,
+    game_status,
+    TRUE, FALSE, game_print_size, game_print,
+    FALSE,			       /* wants_statusbar */
+    FALSE, game_timing_state,
+    REQUIRE_RBUTTON | REQUIRE_NUMPAD,  /* flags */
+};
+
+#ifdef STANDALONE_SOLVER
+
+#include <stdarg.h>
+
+int main(int argc, char **argv)
+{
+    game_params *p;
+    game_state *s;
+    char *id = NULL, *desc, *err;
+    digit *grid;
+    int grade = FALSE;
+    int ret, diff, really_show_working = FALSE;
+
+    while (--argc > 0) {
+        char *p = *++argv;
+        if (!strcmp(p, "-v")) {
+            really_show_working = TRUE;
+        } else if (!strcmp(p, "-g")) {
+            grade = TRUE;
+        } else if (*p == '-') {
+            fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0], p);
+            return 1;
+        } else {
+            id = p;
+        }
+    }
+
+    if (!id) {
+        fprintf(stderr, "usage: %s [-g | -v] <game_id>\n", argv[0]);
+        return 1;
+    }
+
+    desc = strchr(id, ':');
+    if (!desc) {
+        fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
+        return 1;
+    }
+    *desc++ = '\0';
+
+    p = default_params();
+    decode_params(p, id);
+    err = validate_desc(p, desc);
+    if (err) {
+        fprintf(stderr, "%s: %s\n", argv[0], err);
+        return 1;
+    }
+    s = new_game(NULL, p, desc);
+
+    grid = snewn(p->w * p->w, digit);
+
+    /*
+     * When solving a Normal puzzle, we don't want to bother the
+     * user with Hard-level deductions. For this reason, we grade
+     * the puzzle internally before doing anything else.
+     */
+    ret = -1;			       /* placate optimiser */
+    solver_show_working = FALSE;
+    for (diff = 0; diff < DIFFCOUNT; diff++) {
+	memcpy(grid, s->grid, p->w * p->w);
+	ret = solver(&s->par, grid, diff);
+	if (ret <= diff)
+	    break;
+    }
+
+    if (diff == DIFFCOUNT) {
+	if (grade)
+	    printf("Difficulty rating: ambiguous\n");
+	else
+	    printf("Unable to find a unique solution\n");
+    } else {
+	if (grade) {
+	    if (ret == diff_impossible)
+		printf("Difficulty rating: impossible (no solution exists)\n");
+	    else
+		printf("Difficulty rating: %s\n", group_diffnames[ret]);
+	} else {
+	    solver_show_working = really_show_working;
+	    memcpy(grid, s->grid, p->w * p->w);
+	    ret = solver(&s->par, grid, diff);
+	    if (ret != diff)
+		printf("Puzzle is inconsistent\n");
+	    else {
+		memcpy(s->grid, grid, p->w * p->w);
+		fputs(game_text_format(s), stdout);
+	    }
+	}
+    }
+
+    return 0;
+}
+
+#endif
+
+/* vim: set shiftwidth=4 tabstop=8: */