The On-Line Encyclopedia of Bongard Problems

Search: concept:element_wise_symmetry

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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`

BP1092

Has element-wise 180 degree rotational symmetry vs. does not.

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	CROSSREFS	`Adjacent-numbered pages: BP1087 BP1088 BP1089 BP1090 BP1091 * BP1093 BP1094 BP1095 BP1096 BP1097`
	KEYWORD	`nice, anticomputer`
	CONCEPT	`element_wise_symmetry (info \| search),` `rotational_symmetry (info \| search)`
	AUTHOR	`William B Holland`

BP1185

Smaller section tiles the grid (element-wise rotation of tiles allowed) vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1180 BP1181 BP1182 BP1183 BP1184 * BP1186 BP1187 BP1188 BP1189 BP1190`
	KEYWORD	`precise, allsorted, notso, grid, miniworlds`
	CONCEPT	`element_wise_symmetry (info \| search),` `tiling (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1187

Smaller section tiles the grid vs. not so.

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	CROSSREFS	`See BP1185 for the version of this solution where element-wise rotation of tiles is allowed.` `Adjacent-numbered pages: BP1182 BP1183 BP1184 BP1185 BP1186 * BP1188 BP1189 BP1190 BP1191 BP1192`
	KEYWORD	`allsorted, notso, grid`
	CONCEPT	`element_wise_symmetry (info \| search),` `tiling (info \| search)`
	AUTHOR	`Leo Crabbe`

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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