The On-Line Encyclopedia of Bongard Problems

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BP386

Lower shape can be used as a tile to build the upper one vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP381 BP382 BP383 BP384 BP385 * BP387 BP388 BP389 BP390 BP391`
	KEYWORD	`nice, precise, allsorted, left-narrow, perfect, pixelperfect, orderedpair, traditional, preciseworld, left-listable, right-listable`
	CONCEPT	`tiling (info \| search)`
	AUTHOR	`Jago Collins`

BP394

For each colored square only, there exists a path starting on it that covers each square of the figure exactly once vs. there is no path that starts on a colored square and covers each square of the figure exactly once.

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

	CROSSREFS	`Adjacent-numbered pages: BP389 BP390 BP391 BP392 BP393 * BP395 BP396 BP397 BP398 BP399`
	KEYWORD	`hard, nice, solved, traditional, dithering, left-listable, right-listable`
	CONCEPT	`existence (info \| search),` `path (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Jago Collins`

BP904

Rows show all possible ways a certain number of dots can be divided between a certain number of bins vs. not so.

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

	COMMENTS	`The rows in the panels on the right hand side show all the ways you can divide a certain number of dots between a certain number of bins, ignoring which bins they are placed in.`
	CROSSREFS	`Adjacent-numbered pages: BP899 BP900 BP901 BP902 BP903 * BP905 BP906 BP907 BP908 BP909`
	KEYWORD	`solved, left-null, grid, left-listable, right-listable`
	CONCEPT	`permutation (info \| search)`
	AUTHOR	`Molly C Klenzak`

BP926

Numbers of dots in ascending order from left to right vs. numbers of dots neither in ascending nor descending order from left to right.

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

	CROSSREFS	`Adjacent-numbered pages: BP921 BP922 BP923 BP924 BP925 * BP927 BP928 BP929 BP930 BP931`
	KEYWORD	`nice, math, sequence, traditional, left-listable, right-listable`
	CONCEPT	`number (info \| search),` `dot (info \| search)`
	WORLD	`dot_clusters_sequence_horizontal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP931

Some number labels its own position in the sequence from left to right vs. not so.

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

	COMMENTS	`Right examples are called "derangements".`
	CROSSREFS	`Adjacent-numbered pages: BP926 BP927 BP928 BP929 BP930 * BP932 BP933 BP934 BP935 BP936`
	KEYWORD	`handed, leftright, sequence, traditional, left-listable, right-listable`
	CONCEPT	`number (info \| search),` `dot (info \| search),` `self-reference (info \| search)`
	WORLD	`dot_clusters_sequence_horizontal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP956

Nested pairs of brackets vs. other arrangement of brackets (some open brackets are not closed or there are extra closing brackets).

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

	COMMENTS	`Examples on the left are also known as "Dyck words".`
	REFERENCE	`https://en.wikipedia.org/wiki/Dyck_language`
	CROSSREFS	`Adjacent-numbered pages: BP951 BP952 BP953 BP954 BP955 * BP957 BP958 BP959 BP960 BP961`
	KEYWORD	`easy, nice, precise, allsorted, unwordable, notso, sequence, traditional, inductivedefinition, preciseworld, left-listable, right-listable`
	CONCEPT	`recursion (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP997

There exists a loop that passes through every white square once without passing through the black square vs. there exists no such loop.

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

	CROSSREFS	`Adjacent-numbered pages: BP992 BP993 BP994 BP995 BP996 * BP998 BP999 BP1000 BP1001 BP1002`
	KEYWORD	`precise, allsorted, grid, preciseworld, left-listable, right-listable`
	CONCEPT	`path (info \| search)`
	AUTHOR	`James Tanton`

BP1057

Filled subsection divides the grid vs. not so

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

	CROSSREFS	`Adjacent-numbered pages: BP1052 BP1053 BP1054 BP1055 BP1056 * BP1058 BP1059 BP1060 BP1061 BP1062`
	KEYWORD	`math, grid, left-listable, right-listable`
	CONCEPT	`division (info \| search),` `tiling (info \| search)`
	WORLD	`zoom in left`
	AUTHOR	`Jago Collins`

BP1072

Filled subsection is largest square that divides the grid vs. not so

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

	REFERENCE	`https://en.wikipedia.org/wiki/Greatest_common_divisor`
	CROSSREFS	`Any example in this BP is a left example of BP1057.` `Adjacent-numbered pages: BP1067 BP1068 BP1069 BP1070 BP1071 * BP1073 BP1074 BP1075 BP1076 BP1077`
	KEYWORD	`grid, left-listable, right-listable`
	CONCEPT	`division (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP1146

Same number of dots in top row as in leftmost column vs not so.

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

	COMMENTS	`This is a difficult-to-read attempt at making a Bongard Problem about perfect numbers. Grouping columns together to make rectangular arrays, each maximal (most dots possible) rectangular array of a particular height in any given example has the same number of dots in it (a perfect number, in left-sorted cases), and the dot-width of each array represents a particular divisor of that number.` `It is not currently known whether there are a finite amount of examples that would be sorted left.` `Every example in this Bongard Problem corresponds to a distinct natural number. There is not a way of representing the number 1 using the rules of construction for examples in this problem (if the problem were simply "Perfect number of dots vs. other number of dots", the example with 1 dot would be sorted right).`
	REFERENCE	`https://en.wikipedia.org/wiki/Perfect_number`
	CROSSREFS	`Adjacent-numbered pages: BP1141 BP1142 BP1143 BP1144 BP1145 * BP1147 BP1148 BP1149 BP1150 BP1151`
	KEYWORD	`overriddensolution, left-listable, right-listable`
	AUTHOR	`Leo Crabbe`

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