The On-Line Encyclopedia of Bongard Problems

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BP166

Two clusters vs. three clusters.

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	CROSSREFS	`Adjacent-numbered pages: BP161 BP162 BP163 BP164 BP165 * BP167 BP168 BP169 BP170 BP171`
	KEYWORD	`traditional`
	CONCEPT	`number (info \| search),` `dot (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`Multiple options: dot_clusters [smaller \| same \| bigger], point_clusters [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP167

Every cluster has two clusters of dots vs. every cluster has three clusters of dots.

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	CROSSREFS	`Adjacent-numbered pages: BP162 BP163 BP164 BP165 BP166 * BP168 BP169 BP170 BP171 BP172`
	KEYWORD	`traditional`
	CONCEPT	`number (info \| search),` `dot (info \| search),` `recursion (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`Multiple options: dot_clusters [smaller \| same \| bigger], point_clusters [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP318

The numbers of dots can be put into a sequence of consecutive numbers vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP313 BP314 BP315 BP316 BP317 * BP319 BP320 BP321 BP322 BP323`
	KEYWORD	`nice, traditional`
	CONCEPT	`size_increase_decrease (info \| search),` `iteration (info \| search),` `number (info \| search),` `ordinal_orering (info \| search),` `dot (info \| search),` `sequence (info \| search)`
	WORLD	`dot_clusters [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP319

The number of dots in one cluster is a multiple of the other vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP314 BP315 BP316 BP317 BP318 * BP320 BP321 BP322 BP323 BP324`
	KEYWORD	`math, unorderedpair, traditional`
	CONCEPT	`multiple_of (info \| search),` `number (info \| search),` `dot (info \| search),` `proportional (info \| search)`
	WORLD	`two_dot_clusters [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP320

The numbers of dots in the two clusters are approximately equal (log scale) vs. the numbers of dots in the two clusters differ a lot.

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	COMMENTS	`The point is that, on the left, the two groups look about the same to the eye at first glance.` `In left examples the numbers are off by a factor of 7/6 or less vs. in right examples the numbers are off by a factor of 2 or greater.`
	CROSSREFS	`Adjacent-numbered pages: BP315 BP316 BP317 BP318 BP319 * BP321 BP322 BP323 BP324 BP325`
	KEYWORD	`nice, traditional`
	CONCEPT	`numerosity (info \| search),` `similar_number (info \| search),` `similar (info \| search)`
	WORLD	`two_dot_clusters [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP334

Odd number of dots vs. even number of dots.

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	CROSSREFS	`See BP334 for a version of the same idea, but using arbitrary shapes instead of dots.` `Adjacent-numbered pages: BP329 BP330 BP331 BP332 BP333 * BP335 BP336 BP337 BP338 BP339`
	KEYWORD	`precise, allsorted, number, math, left-narrow, right-narrow, right-null, help, traditional, preciseworld`
	CONCEPT	`even_odd (info \| search)`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP384

Square number of dots vs. non-square number of dots.

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	COMMENTS	`All examples in this Problem are a collection of dots.` `An equivalent solution is "Dots can be arranged into a square lattice whose convex hull is a square vs. not so". - Leo Crabbe, Aug 01 2020`
	CROSSREFS	`Adjacent-numbered pages: BP379 BP380 BP381 BP382 BP383 * BP385 BP386 BP387 BP388 BP389`
	EXAMPLE	`A single dot fits because 1 = 11.` `A pair of dots does not fit because there is no integer x such that 2 = xx.`
	KEYWORD	`nice, precise, allsorted, number, math, left-narrow, left-null, help, traditional, preciseworld, collection`
	CONCEPT	`square_number (info \| search)`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP541

Bongard Problems vs. anything else.

BP1

BP2

BP3

BP4

BP541

BP1073

blllmam

cat

nongard

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	COMMENTS	`This refers to all Bongard Problem solution ideas. No need to be a particularly well-made or well-defined Bongard Problem.`
	CROSSREFS	`Adjacent-numbered pages: BP536 BP537 BP538 BP539 BP540 * BP542 BP543 BP544 BP545 BP546`
	KEYWORD	`notso, meta (see left/right), links, world, left-self, right-null, left-it, feedback`
	WORLD	`everything [smaller \| same] zoom in left (bp)`
	AUTHOR	`Aaron David Fairbanks`

BP542

BP Pages on the OEBP vs. anything else.

BP1

BP2

BP3

BP542

BP1073

BP0

nolab

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	CROSSREFS	`Adjacent-numbered pages: BP537 BP538 BP539 BP540 BP541 * BP543 BP544 BP545 BP546 BP547`
	KEYWORD	`notso, meta (see left/right), links, oebp, world, left-self, right-null, left-it, feedback`
	WORLD	`everything [smaller \| same] zoom in left (bppage)`
	AUTHOR	`Aaron David Fairbanks`

BP544

Everything vs. nothing.

	&(%	0	BP1	BP544	BP1073
		dog	nothing

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	COMMENTS	`All ideas and things, with no limits.`
	CROSSREFS	`Adjacent-numbered pages: BP539 BP540 BP541 BP542 BP543 * BP545 BP546 BP547 BP548 BP549`
	KEYWORD	`notso, meta (see left/right), links, world, left-self, right-finite, right-full, left-null, left-it, feedback, experimental, funny`
	CONCEPT	`existence (info \| search)`
	WORLD	`everything [smaller \| same] zoom in left (everything) \| zoom in right (nothing)`
	AUTHOR	`Aaron David Fairbanks`

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