The On-Line Encyclopedia of Bongard Problems

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Identical figures vs. figures not identical.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 232.`
	CROSSREFS	`BP1222 is similar but allows the shapes to be different sizes.` `BP343 is about existence of a pair of identical shapes among many shapes.` `Adjacent-numbered pages: BP52 BP53 BP54 BP55 BP56 * BP58 BP59 BP60 BP61 BP62`
	KEYWORD	`nice, finished, unorderedpair, traditional, bongard`
	CONCEPT	`identical (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Solid dark quadrangles are identical vs. solid dark quadrangles are different.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 233.`
	CROSSREFS	`Adjacent-numbered pages: BP53 BP54 BP55 BP56 BP57 * BP59 BP60 BP61 BP62 BP63`
	KEYWORD	`noisy, finished, traditional, bongard`
	CONCEPT	`identical (info \| search),` `outlined_filled (info \| search),` `square (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `same_shape (info \| search),` `same (info \| search),` `texture (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

No two shapes are the same vs. at least two shapes are the same.

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	CROSSREFS	`BP57 is the same solution except all examples have two shapes.` `Adjacent-numbered pages: BP338 BP339 BP340 BP341 BP342 * BP344 BP345 BP346 BP347 BP348`
	KEYWORD	`traditional`
	CONCEPT	`existence (info \| search),` `identical (info \| search),` `same_shape (info \| search),` `same (info \| search),` `two (info \| search)`
	WORLD	`shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Two of the same object are enclosed in the same space (there is a path between them) vs. not so.

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	COMMENTS	`An "object" is everything within some black boundary.`
	CROSSREFS	`See BP1071 for a version with only squares and with infinite nesting allowed.` `Adjacent-numbered pages: BP972 BP973 BP974 BP975 BP976 * BP978 BP979 BP980 BP981 BP982`
	KEYWORD	`nice, precise, allsorted, creativeexamples, traditional`
	CONCEPT	`separated_regions (info \| search),` `identical (info \| search),` `recursion (info \| search),` `imagined_line_or_curve (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Palindromes vs. not palindromes.

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	COMMENTS	`All examples in this Problem are sequences of graphic symbols. In this Problem, a "palindrome" is taken to be an ordered sequence which is the same read left-to-right as it is read right-to-left. A more formal solution to this Problem could be: "Sequences which are invariant under a permutation which swaps first and last entries, second and second last entries, third and third last entries, ... and so on vs. sequences which are not invariant under the aforementioned permutamation."`
	CROSSREFS	`Adjacent-numbered pages: BP981 BP982 BP983 BP984 BP985 * BP987 BP988 BP989 BP990 BP991`
	KEYWORD	`nice, precise, allsorted, notso, sequence, traditional`
	CONCEPT	`element_wise_symmetry (info \| search),` `identical (info \| search),` `sequence (info \| search),` `same_shape (info \| search),` `same (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Jago Collins`

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