The On-Line Encyclopedia of Bongard Problems

Search: +meta:BP867

Displaying 121-130 of 131 results found.

( prev | next ) page 1 ... 4 5 6 7 8 9 10 11 12 13 14

Sort: id Format: long Filter: (all | no meta | meta) Mode: (words | no words)

Any shape's axis of reflection is shared by another shape vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP1259 BP1260 BP1261 BP1262 BP1263 * BP1265 BP1266 BP1267 BP1268 BP1269`
	KEYWORD	`precise, allsorted, notso, left-narrow`
	CONCEPT	`symmetry (info \| search)`
	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`

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`

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.

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

	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`

BP1270

Straight line can separate the two types of figures vs. not so.

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

	COMMENTS	`This Bongard Problem is a sort of meta-problem. The problems inside the boxes aren't exactly Bongard problems, but they do deal with categorization. The objects must be split into two obvious and distinct groups, but one is not given any examples to work with.`
	CROSSREFS	`The two sides of BP3 are the same as the two sides in the first box.` `Adjacent-numbered pages: BP1265 BP1266 BP1267 BP1268 BP1269 * BP1271 BP1272 BP1273 BP1274 BP1275`
	KEYWORD	`notso`
	AUTHOR	`Ben`

BP1273

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

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

	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.

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

	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`

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 BP1281`
	KEYWORD	`unwordable, notso, arbitrary, sequence`
	CONCEPT	`element_grouping (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1282

If two players take turns moving moving the black circles with the intention of capturing their opponent's piece, one can always "checkmate" the other vs. the game results in a draw if the players play optimally.

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

	COMMENTS	`Players can only move their piece to a node connected to their current position. A win is secured by moving to a node your opponent is occupying.` `Which player that can force a win in left-sorted examples can change depending on who moves first.`
	CROSSREFS	`See BP1284 for an animated Problem about the same game.` `Adjacent-numbered pages: BP1277 BP1278 BP1279 BP1280 BP1281 * BP1283 BP1284 BP1285 BP1286 BP1287`
	KEYWORD	`allsorted, unwordable, notso, teach`
	CONCEPT	`capture_game (info \| search)`
	AUTHOR	`Leo Crabbe`

( prev | next ) page 1 ... 4 5 6 7 8 9 10 11 12 13 14

		Hints
(Greetings from The On-Line Encyclopedia of Bongard Problems!)