The On-Line Encyclopedia of Bongard Problems

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Square divided into four areas of the same size and shape vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP288 BP289 BP290 BP291 BP292 * BP294 BP295 BP296 BP297 BP298`
	KEYWORD	`nice, traditional`
	CONCEPT	`square (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`"Lewis"`

Three objects are identical, the fourth differs vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP298 BP299 BP300 BP301 BP302 * BP304 BP305 BP306 BP307 BP308`
	KEYWORD	`noisy, traditional, fixedgrid`
	CONCEPT	`same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`"Lewis"`

Shapes identical after rotation vs. shapes identical after rotation and mirroring.

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	CROSSREFS	`Adjacent-numbered pages: BP300 BP301 BP302 BP303 BP304 * BP306 BP307 BP308 BP309 BP310`
	KEYWORD	`nice, traditional`
	CONCEPT	`rotation_required (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`"Lewis"`

Left shapes can be placed on top of each other to make right shape vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP319 BP320 BP321 BP322 BP323 * BP325 BP326 BP327 BP328 BP329`
	KEYWORD	`precise, unstable, perfect, pixelperfect, structure, orderedtriplet, traditional`
	CONCEPT	`set_union (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

High approximate similarity vs. lower approximate similarity.

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	CROSSREFS	`Adjacent-numbered pages: BP333 BP334 BP335 BP336 BP337 * BP339 BP340 BP341 BP342 BP343`
	KEYWORD	`spectrum, traditional, continuous`
	CONCEPT	`imperfection_small (info \| search),` `same_shape (info \| search),` `same (info \| search),` `similar_shape (info \| search),` `similar (info \| search)`
	WORLD	`two_shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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`

Same shape up to resizing vs. different shapes.

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	CROSSREFS	`BP57 instead requires the shapes are identical, even in size.` `Adjacent-numbered pages: BP1217 BP1218 BP1219 BP1220 BP1221 * BP1223 BP1224 BP1225 BP1226 BP1227`
	KEYWORD	`stub, precise, allsorted, traditional`
	CONCEPT	`size (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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