The On-Line Encyclopedia of Bongard Problems

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It is possible to deduce the contents of the missing square vs. not so.

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	COMMENTS	`All examples show grids of squares with an image in each square, such that there is some "rule" the images within the grid obey. The "rule" can be about how the images relate to their neighbors, it can involve the position of the images in the grid, and it can involve properties of the grid considered as a whole. One square from somewhere along the edge of the grid is removed.` `Intentionally left out of this Bongard Problem (or left as sorted ambiguously) are cases in which there is no clear rule, or it is not possible to deduce what the intended rule is without seeing more squares (e.g. EX8097). Due to this choice to omit those kinds of examples from the right, another acceptable solution is "it is possible to deduce the contents of the missing square once the underlying rule is understood vs. not so."`
	REFERENCE	`https://en.wikipedia.org/wiki/Raven%27s_Progressive_Matrices`
	CROSSREFS	`BP1258 is very similar: whether ALL squares can be deduced from the rest.` `Adjacent-numbered pages: BP974 BP975 BP976 BP977 BP978 * BP980 BP981 BP982 BP983 BP984`
	KEYWORD	`nice, notso, structure, rules, miniworlds`
	CONCEPT	`convey_enough_information (info \| search),` `choice (info \| search)`
	WORLD	`grid_of_images_with_rule_one_on_edge_missing [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP14

All big individual figures vs. all small individual figures.

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	COMMENTS	`All examples in this Problem show one or more connected figures made up of lines.` `Some big shapes and some small shapes would be ambiguous.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.`
	CROSSREFS	`See BP2 for the same idea using one shape.` `Adjacent-numbered pages: BP9 BP10 BP11 BP12 BP13 * BP15 BP16 BP17 BP18 BP19`
	KEYWORD	`fuzzy, size, stable, finished, traditional, bongard`
	CONCEPT	`all (info \| search),` `length_line_or_curve (info \| search),` `size (info \| search)`
	WORLD	`curves_drawing [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP335

Tessellates the plane vs. does not tessellate the plane.

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	COMMENTS	`EX7152 is an example of a shape than can be stretched in such a way that it no longer tessellates the plane. This is a property that is only exhibited by shapes that tessellate with rotated copies of themselves. - Leo Crabbe, Mar 05 2021`
	CROSSREFS	`Adjacent-numbered pages: BP330 BP331 BP332 BP333 BP334 * BP336 BP337 BP338 BP339 BP340`
	KEYWORD	`nice, stretch, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, pixelperfect, traditional`
	CONCEPT	`infinite_plane (info \| search),` `tessellation (info \| search),` `tiling (info \| search)`
	WORLD	`shape [smaller \| same \| bigger] zoom in left (fill_shape)`
	AUTHOR	`Aaron David Fairbanks`

BP1133

Impossible to realize in 3D space vs. not so.

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	COMMENTS	`Each unit is to be imagined as a flat rigid rod/hoop/triangle/etc.`
	REFERENCE	`https://en.wikipedia.org/wiki/Borromean_rings`
	CROSSREFS	`Similar to BP252.` `Adjacent-numbered pages: BP1128 BP1129 BP1130 BP1131 BP1132 * BP1134 BP1135 BP1136 BP1137 BP1138`
	KEYWORD	`precise`
	CONCEPT	`rigidity (info \| search),` `impossible (info \| search)`
	AUTHOR	`Leo Crabbe`

BP387

Dots can be shared equally between figures vs. dots cannot be shared equally between figures.

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	CROSSREFS	`Adjacent-numbered pages: BP382 BP383 BP384 BP385 BP386 * BP388 BP389 BP390 BP391 BP392`
	KEYWORD	`nice, traditional`
	CONCEPT	`division (info \| search)`
	AUTHOR	`Jago Collins`

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`

BP286

Decreasing in size from top to bottom vs. increasing in size from top to bottom.

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	CROSSREFS	`Adjacent-numbered pages: BP281 BP282 BP283 BP284 BP285 * BP287 BP288 BP289 BP290 BP291`
	KEYWORD	`dual, handed, updown, traditional`
	CONCEPT	`size_increase_decrease (info \| search),` `downward_upward (info \| search),` `regular_irregular_change (info \| search),` `size (info \| search)`
	AUTHOR	`"Lewis"`

BP1136

The removal of any one loop disentangles the whole arrangement vs. not so.

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	COMMENTS	`Left-hand examples are called "Brunnian links".`
	REFERENCE	`https://en.wikipedia.org/wiki/Brunnian_link`
	CROSSREFS	`Adjacent-numbered pages: BP1131 BP1132 BP1133 BP1134 BP1135 * BP1137 BP1138 BP1139 BP1140 BP1141`
	KEYWORD	`precise, hardsort`
	CONCEPT	`knot (info \| search)`
	WORLD	`link [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1224

Grey shape present vs. not.

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	CROSSREFS	`Adjacent-numbered pages: BP1219 BP1220 BP1221 BP1222 BP1223 * BP1225 BP1226 BP1227 BP1228 BP1229`
	KEYWORD	`stub, notso, dithering`
	CONCEPT	`existence (info \| search),` `texture (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP860

Finitely many copies of the shape can be arranged such that they are locked together vs. not so.

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	CROSSREFS	`This is a generalisation of BP861.` `Adjacent-numbered pages: BP855 BP856 BP857 BP858 BP859 * BP861 BP862 BP863 BP864 BP865`
	KEYWORD	`hard, nice, stub, precise, stretch, unstable, hardsort, challenge, creativeexamples, perfect, pixelperfect`
	CONCEPT	`tiling (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

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