The On-Line Encyclopedia of Bongard Problems

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The convex hull of the crosses forms an equilateral triangle vs. the convex hull of the crosses does not form an equilateral triangle.

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

	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 241.`
	CROSSREFS	`Adjacent-numbered pages: BP77 BP78 BP79 BP80 BP81 * BP83 BP84 BP85 BP86 BP87`
	KEYWORD	`noisy, notso, finished, traditional, bongard`
	CONCEPT	`convex_hull (info \| search),` `equilateral_triangle (info \| search),` `triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP1005

The collection of dot clumps has the same numerical property as each of the dot clumps vs. not so.

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

	CROSSREFS	`This is a version of BP999 with only numbers.` `Contrast BP1006, which is very similar.` `Adjacent-numbered pages: BP1000 BP1001 BP1002 BP1003 BP1004 * BP1006 BP1007 BP1008 BP1009 BP1010`
	KEYWORD	`nice, notso, hardsort, left-narrow, rules`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

BP1266

Angles either only increase or only decrease as one moves along the curve vs. not so.

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

	COMMENTS	`It does not matter which end of the curve one starts from, nor which "side" angles are measured from, so long as the side is kept consistent.`
	CROSSREFS	`Adjacent-numbered pages: BP1261 BP1262 BP1263 BP1264 BP1265 * BP1267 BP1268 BP1269 BP1270 BP1271`
	KEYWORD	`allsorted, notso, traditional`
	CONCEPT	`angle (info \| search),` `size_increase_decrease (info \| search)`
	AUTHOR	`Leo Crabbe`

BP223

Large black region if completed is a circle vs. large black region if completed is an ellipse.

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

	CROSSREFS	`Adjacent-numbered pages: BP218 BP219 BP220 BP221 BP222 * BP224 BP225 BP226 BP227 BP228`
	KEYWORD	`noisy, perfect, traditional`
	CONCEPT	`imperfection_small (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP1258

It is possible to deduce the contents of any square from the rest vs. it is not.

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

	CROSSREFS	`BP979 is very similar: whether a particular square can be deduced from the rest.` `Adjacent-numbered pages: BP1253 BP1254 BP1255 BP1256 BP1257 * BP1259 BP1260 BP1261 BP1262 BP1263`
	KEYWORD	`notso, rules, grid, miniworlds`
	CONCEPT	`convey_enough_information (info \| search),` `choice (info \| search)`
	WORLD	`grid_of_images_with_rule [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP311

Number of sides minus number of pluses = 3 vs. number of sides minus number of pluses = 4.

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

	CROSSREFS	`Adjacent-numbered pages: BP306 BP307 BP308 BP309 BP310 * BP312 BP313 BP314 BP315 BP316`
	KEYWORD	`traditional`
	CONCEPT	`subtraction (info \| search),` `number (info \| search)`
	AUTHOR	`Jakub Štepo`

BP902

This Bongard Problem vs. anything else.

BP902

BP1

becious

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

	COMMENTS	`Although this Bongard Problem is self-referential, it's only because of the specific phrasing of the solution. "BP902 vs. anything else" would also work. The number 902 could have been chosen coincidentally.`
	CROSSREFS	`See BP953, BP959.` `Adjacent-numbered pages: BP897 BP898 BP899 BP900 BP901 * BP903 BP904 BP905 BP906 BP907`
	KEYWORD	`notso, meta (see left/right), links, left-self, left-narrow, left-finite, left-full, right-null, right-it, invalid, experimental, funny`
	CONCEPT	`self-reference (info \| search),` `specificity (info \| search)`
	WORLD	`everything [smaller \| same] zoom in left (bp902)`
	AUTHOR	`Leo Crabbe`

BP92

The chain does not branch vs. the chain branches.

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

	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 244.`
	CROSSREFS	`Adjacent-numbered pages: BP87 BP88 BP89 BP90 BP91 * BP93 BP94 BP95 BP96 BP97`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`all (info \| search),` `branch_point (info \| search),` `collinear (info \| search),` `existence (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP47

Triangle inside of the circle vs. circle inside of the triangle.

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

	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 229.`
	CROSSREFS	`Adjacent-numbered pages: BP42 BP43 BP44 BP45 BP46 * BP48 BP49 BP50 BP51 BP52`
	KEYWORD	`finished, traditional, viceversa, bongard`
	CONCEPT	`inside (info \| search),` `triangle (info \| search)`
	WORLD	`circle_triangle_outlines_nest [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP965

If you place the image on top of itself so that it lines up with itself exactly within a small region, it also lines up everywhere else vs. not so.

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

	COMMENTS	`Rotations are allowed. To avoid confusion about whether reflections are allowed, no examples are included on the right that require reflections to match up with themselves locally but not globally; no examples are included on the left that can match up with themselves locally but not globally using a reflection.` `Only parts of ellipses are used, and only one type of ellipse per image, to make everything easier to read and reason about.`
	CROSSREFS	`See BP1246 for a variation on this idea where instead of lining the image up with itself along arbitrarily small regions, you line the image up with itself along individual separate objects.` `Adjacent-numbered pages: BP960 BP961 BP962 BP963 BP964 * BP966 BP967 BP968 BP969 BP970`
	KEYWORD	`hard, precise, distractingworld, perfect`
	CONCEPT	`local_global (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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