The On-Line Encyclopedia of Bongard Problems

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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`

BP1275

There is a way of grouping elements into (more than one) equal-sized blocks such that no block appears twice vs. there exists no such grouping.

(edit; present; nest [left/right]; search; history)

	COMMENTS	`Sequences with a prime number of elements are sorted left when all their elements are unique, and sorted right otherwise.`
	CROSSREFS	`Adjacent-numbered pages: BP1270 BP1271 BP1272 BP1273 BP1274 * BP1276 BP1277 BP1278 BP1279 BP1280`
	EXAMPLE	`The sequence ABBABB would be sorted left, as it could be grouped into (AB)(BA)(BB), where each block is unique.`
	KEYWORD	`precise, unwordable, notso, sequence, miniworlds`
	CONCEPT	`element_grouping (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1276

Ways of representing the sequence "ABABCBACCBAC" by grouping its elements into equal-sized blocks and relabelling them (identical blocks are represented by the same element) vs. representations of different sequences.

(edit; present; nest [left/right]; search; history)

	COMMENTS	`The solver isn't expected to word their solution as it is put above, but to notice that the sequences on the left all "agree" with each other under the aforementioned grouping rule. The 12-element sequence in EX10249 can be "squashed down" into the 6-element sequence in EX10251, which in turn can be "squashed down" into the 3-element sequence in EX10252.`
	CROSSREFS	`Compare to BP121` `Adjacent-numbered pages: BP1271 BP1272 BP1273 BP1274 BP1275 * BP1277 BP1278 BP1279 BP1280`
	KEYWORD	`unwordable, notso, arbitrary, sequence`
	CONCEPT	`element_grouping (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1278

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