The On-Line Encyclopedia of Bongard Problems

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BP1266

Angles either only increase or only decrease as one moves along the curve vs. not so.

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	COMMENTS	`It does not matter which end of the curve one starts from, nor which "side" angles are measured from, so long as the side is kept consistent.`
	CROSSREFS	`Adjacent-numbered pages: BP1261 BP1262 BP1263 BP1264 BP1265 * BP1267 BP1268 BP1269 BP1270 BP1271`
	KEYWORD	`allsorted, notso, traditional`
	CONCEPT	`angle (info \| search),` `size_increase_decrease (info \| search)`
	AUTHOR	`Leo Crabbe`

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`

BP1278

There is a way of dividing the grid into (more than one) equal-sized blocks such that no block appears more than once vs. there exists no such way of dividing the grid.