132:
A 2×2 room in the corner of the grid containing a '2' must have one painted cell in the grid corner and the second painted square diagonally outward from the corner. As painted squares may not share a side (Rule 1), the only alternative would disconnect the forced white cell in the corner, violating
62:
Some of the cells in the puzzle are to be painted black; the object of the puzzle is to determine for each cell if it must be painted or must be left blank (remaining white). In practice, it is often easier to mark known "blank" cells in some way—for example, by placing a dot in the center of
58:
is played on a rectangular grid of cells with no standard size; the grid is divided into variously sized rectangular "rooms" by bold lines following the edges of the cells. Some rooms may contain a single number, typically printed in their upper-left cell; as originally designed, every room was
109:
A section of (orthogonally) contiguous white cells cannot be cut off from the rest of the grid (from Rule 2). Black cells may not form a diagonal split across the grid nor a closed loop; any cell that would complete such a "short circuit" must be white
136:
A 2×3 room with the 3-cell side along a grid border containing a '3' must have a painted cell in the center of the 3-cell side along the border and the other two in the opposite corners of the room, for similar reasons to the
86:
Rule 5: Where a straight (orthogonal) line of connected white cells is formed, it must not contain cells from more than two rooms—in other words, any such line of white cells which connects three or more rooms is
114:
More complex puzzles require combining Rule 1 and Rule 2 to make progress without guessing; the key is recognizing where the cells must assume one of two checkered patterns and one leads to a short circuit.
166:
is played like
Heyawake, but rooms are not necessarily rectangular. Orthogonal lines of white cells may not exit and re-enter a room; i.e. such lines may not straddle more than one region boundary.
126:
Rule 5 is the defining rule of the puzzle; black cells must be placed to prevent any (orthogonal) lines of white cells that cross two room borders ("spanners").
129:
Numbered rooms typically provide solvers a starting place, among other deductions. The following are the simplest examples of rooms defined at the onset:
106:
If it is discovered that a cell is painted black, it is immediately known that all of the four (orthogonally) adjacent cells must be white (from Rule 1).
140:
A 1×3 room containing a '2' must have the two end cells painted, as a painted centre cell would force a breach of rule 1. More generally, a 1×(2
180:) is played like Heyawake, but clues indicate whether the pattern of black cells in a room is rotationally symmetric around its centre or not.
271:
17:
190:
290:
198:
319:
314:
193:
of
Heyawake has been analyzed: deciding for a given instance of Heyawake whether there exists a solution to the puzzle is
70:
Rule 1: Painted cells may never be orthogonally connected (they may not share a side, although they can touch diagonally).
213:
197:. An interpretation of this theoretical result in layman's terms is that this puzzle is as hard to solve as the
151:
A 3×3 room containing a '5' must have a checkered pattern, with painted cells in all corners and the center.
309:
36:
80:
Rule 3: A number indicates exactly how many painted cells there must be in that particular room.
267:
28:
259:
202:
294:
244:
303:
83:
Rule 4: A room which has no number may contain any number of painted cells, or none.
287:
32:
263:
194:
59:
numbered, but this is rarely necessary for solving and is no longer followed.
245:"The Troubles of Interior Design–A Complexity Analysis of the Game Heyawake"
74:
16:
102:
puzzles, and thus these puzzles share some of their solving methods:
98:
252:
Proceedings, 4th
International Conference on Fun with Algorithms,
15:
253:
73:
Rule 2: All white cells must be interconnected (form a single
43:
puzzles have been published by Nikoli. It first appeared in
96:
Note that the first two rules also apply to (for example)
66:
The following rules determine which cells are which:
31:: へやわけ, "divided rooms") is a binary-determination
258:. Springer, Berlin/Heidelberg. pp. 198–212.
39:. As of 2013, five books consisting entirely of
201:, which is a well studied difficult problem in
148:must have every other cell within it painted.
8:
223:
243:Holzer, Markus; Ruepp, Oliver (2007).
7:
118:The remaining rules differentiate
14:
199:Boolean satisfiability problem
122:from other "dynasty" puzzles:
1:
264:10.1007/978-3-540-72914-3_18
214:List of Nikoli puzzle types
45:Puzzle Communication Nikoli
336:
230:M. Holzer, O. Ruepp (2007)
288:Nikoli's page on Heyawake
191:computational complexity
185:Computational complexity
144:−1) room containing an
47:#39 (September 1992).
21:
19:
320:Japanese board games
315:NP-complete problems
293:2013-11-09 at the
22:
273:978-3-540-72913-6
170:Symmetry Heyawake
20:A Heyawake puzzle
327:
277:
249:
231:
228:
203:computer science
92:Solution methods
335:
334:
330:
329:
328:
326:
325:
324:
300:
299:
295:Wayback Machine
284:
274:
247:
242:
239:
234:
229:
225:
221:
211:
187:
172:(also known as
160:
94:
53:
12:
11:
5:
333:
331:
323:
322:
317:
312:
302:
301:
298:
297:
283:
282:External links
280:
279:
278:
272:
238:
235:
233:
232:
222:
220:
217:
210:
207:
186:
183:
182:
181:
167:
159:
156:
155:
154:
153:
152:
149:
138:
134:
127:
112:
111:
107:
93:
90:
89:
88:
84:
81:
78:
71:
52:
49:
13:
10:
9:
6:
4:
3:
2:
332:
321:
318:
316:
313:
311:
310:Logic puzzles
308:
307:
305:
296:
292:
289:
286:
285:
281:
275:
269:
265:
261:
257:
255:
246:
241:
240:
236:
227:
224:
218:
216:
215:
208:
206:
204:
200:
196:
192:
184:
179:
175:
171:
168:
165:
162:
161:
157:
150:
147:
143:
139:
135:
131:
130:
128:
125:
124:
123:
121:
116:
108:
105:
104:
103:
101:
100:
91:
85:
82:
79:
76:
72:
69:
68:
67:
64:
60:
57:
50:
48:
46:
42:
38:
35:published by
34:
30:
26:
18:
251:
226:
212:
188:
177:
173:
169:
163:
145:
141:
119:
117:
113:
97:
95:
65:
61:
55:
54:
44:
40:
33:logic puzzle
24:
23:
195:NP-complete
304:Categories
237:References
87:forbidden.
63:the cell.
164:Heyawacky
75:polyomino
291:Archived
209:See also
174:ekawayeH
158:Variants
120:Heyawake
110:instead.
56:Heyawake
41:Heyawake
29:Japanese
25:Heyawake
178:Ayaheya
133:Rule 2.
270:
137:above.
99:Hitori
37:Nikoli
248:(PDF)
219:Notes
51:Rules
268:ISBN
256:4475
254:LNCS
189:The
176:and
260:doi
306::
266:.
250:.
205:.
77:).
276:.
262::
146:n
142:n
27:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
