The On-Line Encyclopedia of Bongard Problems

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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)`
	WORLD	`zoom in left \| zoom in right`
	AUTHOR	`Jago Collins`

BP1086

Endpoints of curve have the same height vs. not so.

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	REFERENCE	`Solution idea seen here: https://justpuzzles.wordpress.com/2019/07/05/bongard-problem-36-2.`
	CROSSREFS	`Adjacent-numbered pages: BP1081 BP1082 BP1083 BP1084 BP1085 * BP1087 BP1088 BP1089 BP1090 BP1091`
	KEYWORD	`nice, rotate, stretch, left-narrow, traditional`
	CONCEPT	`same (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Teun Spaans`

BP1138

Each attribute is shared by every group or none vs. some attribute is shared by exactly two groups

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	COMMENTS	`Attributes are shading, shape, and number.` `There are always three groups.` `This problem is related to the card game Set.`
	CROSSREFS	`Adjacent-numbered pages: BP1133 BP1134 BP1135 BP1136 BP1137 * BP1139 BP1140 BP1141 BP1142 BP1143`
	KEYWORD	`nice, precise, allsorted, notso, preciseworld`
	CONCEPT	`all (info \| search),` `number (info \| search),` `same (info \| search),` `two (info \| search),` `three (info \| search)`
	AUTHOR	`William B Holland`

BP1222

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`

BP1260

Same transformation applied to circle, triangle, and square vs. different transformations applied.

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	CROSSREFS	`BP839 is about applying opposite transformations to a single object.` `Adjacent-numbered pages: BP1255 BP1256 BP1257 BP1258 BP1259 * BP1261 BP1262 BP1263 BP1264 BP1265`
	KEYWORD	`easy, nice, abstract, arbitrary, anticomputer, left-null, structure, orderedtriplet, traditional, rules`
	CONCEPT	`circle (info \| search),` `analogy (info \| search),` `square (info \| search),` `same (info \| search),` `triangle (info \| search),` `function (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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.

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	COMMENTS	`Any palindrome would be sorted left, except strings of length zero or one.`
	CROSSREFS	`Adjacent-numbered pages: BP1263 BP1264 BP1265 BP1266 BP1267 * BP1269`
	KEYWORD	`precise, allsorted, unwordable, sequence, traditional, miniworlds`
	CONCEPT	`element_wise_symmetry (info \| search),` `sequence (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	WORLD	`zoom in left \| zoom in right`
	AUTHOR	`Leo Crabbe`

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