The On-Line Encyclopedia of Bongard Problems

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BP1157

The order in which the objects in the top half are combined to make the object in the lower half matters vs. not so.

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	COMMENTS	`Operations depicted in right-sorted examples are called "commutative".` `"Order matters" here means that if the objects in the top half were to switch places, the output would look different.`
	REFERENCE	`https://en.wikipedia.org/wiki/Commutative_property`
	CROSSREFS	`Adjacent-numbered pages: BP1152 BP1153 BP1154 BP1155 BP1156 * BP1158 BP1159 BP1160 BP1161 BP1162`
	KEYWORD	`nice, abstract, unwordable, notso, structure, rules, miniworlds`
	CONCEPT	`function (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1175

Each symbol appears once in any given row or column vs. not so.

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	REFERENCE	`https://en.wikipedia.org/wiki/Latin_square`
	CROSSREFS	`Adjacent-numbered pages: BP1170 BP1171 BP1172 BP1173 BP1174 * BP1176 BP1177 BP1178 BP1179 BP1180`
	KEYWORD	`precise, traditional, grid, miniworlds, dithering`
	AUTHOR	`Leo Crabbe`

BP1185

Smaller section tiles the grid (element-wise rotation of tiles allowed) vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1180 BP1181 BP1182 BP1183 BP1184 * BP1186 BP1187 BP1188 BP1189 BP1190`
	KEYWORD	`precise, allsorted, notso, grid, miniworlds`
	CONCEPT	`element_wise_symmetry (info \| search),` `tiling (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1191

One natural way of matching up the two collections vs. multiple natural ways of matching up the two collections.

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	COMMENTS	`Jago originally designed this as a triptych. EX9655, EX9656, and EX9657 belong in a third category displayed further right of the two categories shown here. The third category is "all possible ways of matching are equally natural". - Aaron David Fairbanks, Apr 18 2022`
	CROSSREFS	`Adjacent-numbered pages: BP1186 BP1187 BP1188 BP1189 BP1190 * BP1192 BP1193 BP1194 BP1195 BP1196`
	KEYWORD	`nice, abstract, creativeexamples, structure, miniworlds, dithering`
	AUTHOR	`Jago Collins`

BP1257

The rule is about squares having a certain relationship with their neighbors vs. it is not.

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	COMMENTS	`"Local vs. global."` `For clarity, rules involving diagonal neighbors or squares more than one step away are never used.` `The similar solution "Each square can be deduced from its neighbors vs. not so" does not quite work; for example EX8114 would then not fit left. See also BP1258 ("Each square can be deduced from the rest vs. not so").`
	CROSSREFS	`Adjacent-numbered pages: BP1252 BP1253 BP1254 BP1255 BP1256 * BP1258 BP1259 BP1260 BP1261 BP1262`
	KEYWORD	`structure, rules, grid, miniworlds`
	CONCEPT	`local_global (info \| search)`
	WORLD	`grid_of_images_with_rule [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1258

It is possible to deduce the contents of any square from the rest vs. it is not.

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	CROSSREFS	`BP979 is very similar: whether a particular square can be deduced from the rest.` `Adjacent-numbered pages: BP1253 BP1254 BP1255 BP1256 BP1257 * BP1259 BP1260 BP1261 BP1262 BP1263`
	KEYWORD	`notso, rules, grid, miniworlds`
	CONCEPT	`convey_enough_information (info \| search),` `choice (info \| search)`
	WORLD	`grid_of_images_with_rule [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1259

Rule is the same for rows as it is for columns vs. not

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	CROSSREFS	`All examples on the left are chosen so that rotating or flipping the grid in any way would result in a grid satisfying the same rule.` `Adjacent-numbered pages: BP1254 BP1255 BP1256 BP1257 BP1258 * BP1260 BP1261 BP1262 BP1263 BP1264`
	KEYWORD	`notso, rules, grid, miniworlds`
	WORLD	`grid_of_images_with_rule [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1268

Palindromic when elements are grouped into (more than one) equal-sized blocks vs. no grouping of elements into (more than one) equal-sized blocks is palindromic.

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	COMMENTS	`Any palindrome would be sorted left, except strings of length zero or one.`
	CROSSREFS	`Adjacent-numbered pages: BP1263 BP1264 BP1265 BP1266 BP1267 * BP1269 BP1270 BP1271 BP1272 BP1273`
	KEYWORD	`precise, allsorted, unwordable, notso, sequence, traditional, miniworlds`
	CONCEPT	`element_wise_symmetry (info \| search),` `element_grouping (info \| search),` `sequence (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Leo Crabbe`

BP1273

Sequence contains each possible way its distinct elements can be arranged as a subsequence vs. not so.

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	REFERENCE	`https://en.wikipedia.org/wiki/Superpermutation`
	CROSSREFS	`Adjacent-numbered pages: BP1268 BP1269 BP1270 BP1271 BP1272 * BP1274 BP1275 BP1276 BP1277 BP1278`
	EXAMPLE	`There are 6 ways of arranging the letters A, B and C: ABC, ACB, BAC, BCA, CAB, and CBA. The string "ABCABACBA" contains each of these as a substring, and would therefore be sorted left.`
	KEYWORD	`precise, allsorted, notso, sequence, traditional, miniworlds`
	CONCEPT	`sequence (info \| search),` `overlap (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1274

Reversing the sequence permutes the objects vs. not.

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	COMMENTS	`Equivalently, some permutation of the objects reverses the sequence vs. not.` `Palindromes fit left. Strings of distinct objects repeated any number of times fit left.`
	CROSSREFS	`Adjacent-numbered pages: BP1269 BP1270 BP1271 BP1272 BP1273 * BP1275 BP1276 BP1277 BP1278 BP1279`
	KEYWORD	`nice, precise, allsorted, notso, sequence, miniworlds`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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