The On-Line Encyclopedia of Bongard Problems

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Archimedean tiling (regular polygons, all vertices look the same) versus two-uniform tiling (regular polygons, two different kinds of vertex).

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP806 BP807 BP808 BP809 BP810 * BP812 BP813 BP814 BP815 BP816`
	KEYWORD	`nice, math`
	CONCEPT	`infinite_plane (info \| search),` `tiling (info \| search),` `symmetry (info \| search)`
	WORLD	`wallpaper_tiling [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP899

Regions in drawing (ignore background) can be coloured using three or fewer colours such that no adjacent regions are coloured the same colour vs. four colours are required.

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	COMMENTS	`This Problem is related to the four colour theorem.`
	CROSSREFS	`Adjacent-numbered pages: BP894 BP895 BP896 BP897 BP898 * BP900 BP901 BP902 BP903 BP904`
	KEYWORD	`hard, nice, math`
	CONCEPT	`separated_regions (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP206

Curve ends in a roughly up or down direction vs. curve ends in a roughly left or right direction.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP201 BP202 BP203 BP204 BP205 * BP207 BP208 BP209 BP210 BP211`
	KEYWORD	`traditional`
	CONCEPT	`downward_upward (info \| search),` `slope_at_endpoint (info \| search),` `line_or_curve_endpoint (info \| search),` `horizontal (info \| search),` `leftward_rightward (info \| search),` `tangent_absolute_direction (info \| search),` `absolute_direction (info \| search),` `vertical (info \| search),` `direction (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP2

Big vs. small.

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	COMMENTS	`The meaning of "big" left intentionally vague. There are various specific ways to define size, such as diameter, minimum distance between points on edge, and size of smallest bounding circle.` `All examples in this Bongard Problem are single simple shapes, either outlines or solid black.` `All examples on the same side are approximately the same size.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.`
	CROSSREFS	`Adjacent-numbered pages: BP1 * BP3 BP4 BP5 BP6 BP7`
	KEYWORD	`easy, nice, fuzzy, spectrum, size, stable, finished, traditional, continuous, bongard`
	CONCEPT	`size (info \| search)`
	WORLD	`outline_or_fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP318

The numbers of dots can be put into a sequence of consecutive numbers vs. not so.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP313 BP314 BP315 BP316 BP317 * BP319 BP320 BP321 BP322 BP323`
	KEYWORD	`nice, traditional`
	CONCEPT	`size_increase_decrease (info \| search),` `iteration (info \| search),` `number (info \| search),` `ordinal_orering (info \| search),` `dot (info \| search),` `sequence (info \| search)`
	WORLD	`dot_clusters [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP382

No knot (unknot) vs. knot.

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	COMMENTS	`To hint at the solution, left examples can be arranged in a sequence to show the unknot tying itself.`
	CROSSREFS	`Adjacent-numbered pages: BP377 BP378 BP379 BP380 BP381 * BP383 BP384 BP385 BP386 BP387`
	KEYWORD	`nice, math, anticomputer, help, traditional`
	CONCEPT	`knot (info \| search),` `topological_transformation (info \| search)`
	WORLD	`knot [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1240

Contains an un-nested white rectangle vs doesn't

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	CROSSREFS	`Adjacent-numbered pages: BP1235 BP1236 BP1237 BP1238 BP1239 * BP1241 BP1242 BP1243 BP1244 BP1245`
	CONCEPT	`existence (info \| search)`
	AUTHOR	`Leo Crabbe`

BP861

Shape can be combined with a copy of itself such that they are locked together vs. not so.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`See BP860 for the more general version of this solution.` `Adjacent-numbered pages: BP856 BP857 BP858 BP859 BP860 * BP862 BP863 BP864 BP865 BP866`
	KEYWORD	`nice, precise, unstable, perfect, pixelperfect`
	CONCEPT	`tiling (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP226

What comes out of black circle has a clockwise direction vs. not so.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP221 BP222 BP223 BP224 BP225 * BP227 BP228 BP229 BP230 BP231`
	KEYWORD	`traditional`
	CONCEPT	`turn_orientation (info \| search),` `protrusion (info \| search),` `rotational_direction (info \| search),` `direction (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP1226

Three identical elements vs. other number of identical elements.

(edit; present; nest [left/right]; search; history)

	COMMENTS	`Based on BP91, which is the same, except for that the right side is "four identical elements".`
	CROSSREFS	`Adjacent-numbered pages: BP1221 BP1222 BP1223 BP1224 BP1225 * BP1227 BP1228 BP1229 BP1230 BP1231`
	KEYWORD	`stub, arbitrary, number, traditional`
	CONCEPT	`number (info \| search),` `three (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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