The On-Line Encyclopedia of Bongard Problems

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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 BP1270 BP1271 BP1272 BP1273`
	KEYWORD	`precise, allsorted, unwordable, notso, sequence, traditional, miniworlds`
	CONCEPT	`element_wise_symmetry (info \| search),` `element_grouping (info \| search),` `sequence (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Leo Crabbe`

BP351

Discrete quantity vs. continuous quantity.

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	CROSSREFS	`See BP873 for the version with Bongard Problems.` `Adjacent-numbered pages: BP346 BP347 BP348 BP349 BP350 * BP352 BP353 BP354 BP355 BP356`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules`
	CONCEPT	`size_increase_decrease (info \| search),` `discrete_continuous (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger] zoom in left (constant_change_discrete_seq_increase_right)`
	AUTHOR	`Aaron David Fairbanks`

BP323

Jigsaw puzzle pieces can be assembled into a square vs. jigsaw puzzle pieces cannot be assembled into a square.

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	COMMENTS	`Although it takes time to check each individual example, the right answer is likely the first thing a person would think of upon seeing this.`
	CROSSREFS	`Adjacent-numbered pages: BP318 BP319 BP320 BP321 BP322 * BP324 BP325 BP326 BP327 BP328`
	KEYWORD	`notso, hardsort`
	CONCEPT	`jigsaw_puzzle (info \| search),` `tiling (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP21

Small shape present vs. all shapes large.

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	COMMENTS	`All examples in this problem include three or fewer outlines of circles and (non-skinny) triangles.`
	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 220.`
	CROSSREFS	`Adjacent-numbered pages: BP16 BP17 BP18 BP19 BP20 * BP22 BP23 BP24 BP25 BP26`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`existence (info \| search),` `size (info \| search)`
	WORLD	`circle_triangle_outlines [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP551

Unstable balance vs. not

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	REFERENCE	`https://en.wikipedia.org/wiki/Stability_theory`
	CROSSREFS	`Adjacent-numbered pages: BP546 BP547 BP548 BP549 BP550 * BP552 BP553 BP554 BP555 BP556`
	EXAMPLE	`The classic example is a pendulum with a solid rod (instead of a string) which has a stable balance point at the bottom of its swing, where if you move the pendulum slightly it will swing back towards that balanced state. However, theoretically the pendulum can also be balanced pointing directly up. In this case, if you move the pendulum slightly it will swing down away from that upwards balanced state.`
	KEYWORD	`updown, rotate, physics, anticomputer, perfect`
	CONCEPT	`tumbles_or_stays_put (info \| search),` `gravity (info \| search)`
	AUTHOR	`Jago Collins`

BP54

A cross, circle, and triangle arranged counterclockwise vs. a cross, circle, and triangle arranged clockwise.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 231.`
	CROSSREFS	`Adjacent-numbered pages: BP49 BP50 BP51 BP52 BP53 * BP55 BP56 BP57 BP58 BP59`
	KEYWORD	`dual, handed, finished, orderedtriplet, traditional, bongard`
	CONCEPT	`turn_orientation (info \| search),` `rotational_direction (info \| search),` `triangle (info \| search),` `direction (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP159

Two clusters of 2+3, middle shape must be seen as rectangle (AND only one linelike shape) vs. two clusters of 2+3, middle shape must be seen as piece of straight line (AND more than one linelike shape).

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	CROSSREFS	`Adjacent-numbered pages: BP154 BP155 BP156 BP157 BP158 * BP160 BP161 BP162 BP163 BP164`
	KEYWORD	`convoluted, unwordable`
	CONCEPT	`number (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP1066

Some region has one box in it vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1061 BP1062 BP1063 BP1064 BP1065 * BP1067 BP1068 BP1069 BP1070 BP1071`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `one (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP137

Dots equal in number to the sides of the closed region vs. dots unequal in number to the sides of the closed region.

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	CROSSREFS	`Adjacent-numbered pages: BP132 BP133 BP134 BP135 BP136 * BP138 BP139 BP140 BP141 BP142`
	KEYWORD	`left-null, traditional`
	CONCEPT	`same_number (info \| search),` `same (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP144

Two clusters of three and two: different features (including clustering) yield different 3-2 splits vs. two clusters of three and two: different features yield the same 3-2 split.

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	CROSSREFS	`Adjacent-numbered pages: BP139 BP140 BP141 BP142 BP143 * BP145 BP146 BP147 BP148 BP149`
	KEYWORD	`nice, traditional, miniworlds`
	CONCEPT	`and (info \| search),` `number (info \| search),` `separable_entangled (info \| search),` `feature_cluster (info \| search),` `shape_cluster (info \| search),` `cluster (info \| search),` `two (info \| search),` `three (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

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