The On-Line Encyclopedia of Bongard Problems

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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.

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

CROSSREFS

2D version of BP1275.

Adjacent-numbered pages: BP1273 BP1274 BP1275 BP1276 BP1277 * BP1279 BP1280 BP1281 BP1282 BP1283

KEYWORD

precise, traditional, grid

AUTHOR

Leo Crabbe

BP1277

Bongard Problem with solution relating to concept: element grouping vs. Bongard Problem unrelated to this concept.

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

	CROSSREFS	`Adjacent-numbered pages: BP1272 BP1273 BP1274 BP1275 BP1276 * BP1278 BP1279 BP1280 BP1281 BP1282`
	KEYWORD	`meta (see left/right), metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "element_grouping"`
	WORLD	`bp [smaller \| same \| bigger]`
	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 BP1281`
	KEYWORD	`unwordable, notso, arbitrary, sequence`
	CONCEPT	`element_grouping (info \| search)`
	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`

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`

BP1269

Identical pairs of symbols are always on opposite sides of the cube (when assembled) vs. some identical symbols are next to each other on the cube.

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

	CROSSREFS	`Adjacent-numbered pages: BP1264 BP1265 BP1266 BP1267 BP1268 * BP1270 BP1271 BP1272 BP1273 BP1274`
	KEYWORD	`left-finite, right-finite, finishedexamples, preciseworld`
	CONCEPT	`cube (info \| search),` `correspondence (info \| search),` `3d_net (info \| search),` `3d_solid (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`

BP1267

Any two lines intersect, and no three lines share an intersection point vs. not so.

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

	COMMENTS	`Left-sorted examples divide the plane into a maximal amount of disconnected white regions by a given number of "cuts". The number of regions in one of these examples will be the nth value of of the Lazy Caterer sequence ( https://oeis.org/A000124 ), where n is the number of lines.`
	REFERENCE	`https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence`
	CROSSREFS	`Adjacent-numbered pages: BP1262 BP1263 BP1264 BP1265 BP1266 * BP1268 BP1269 BP1270 BP1271 BP1272`
	KEYWORD	`precise, allsorted, notso, perfect`
	AUTHOR	`Leo Crabbe`

BP1266

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

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

	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`

BP1265

Visual Bongard Problems about unsorted collections of objects vs. other visual Bongard Problems.

	BP343	BP347	BP349	BP379	BP380	BP384
	BP792

?
BP824

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

	COMMENTS	`Left-sorted Bongard Problems have the keyword "collection" on the OEBP.` `A Problem is sorted left if its examples typically multiple objects, and the solution pertains to the way properties of the objects interrelate. If the positions of objects are relevant to the solution (see "sequence" Problems: BP929), then the Problem is sorted right.`
	CROSSREFS	`Adjacent-numbered pages: BP1260 BP1261 BP1262 BP1263 BP1264 * BP1266 BP1267 BP1268 BP1269 BP1270`
	KEYWORD	`meta (see left/right), links, keyword`
	AUTHOR	`Leo Crabbe`

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