The On-Line Encyclopedia of Bongard Problems

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Empty square present vs. no square present.

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	CROSSREFS	`Nearly identical to BP1221, which is the same except non-empty squares are allowed.` `See BP24 for "circle present vs. not".` `Adjacent-numbered pages: BP1204 BP1205 BP1206 BP1207 BP1208 * BP1210 BP1211 BP1212 BP1213 BP1214`
	KEYWORD	`stub, left-narrow, traditional`
	CONCEPT	`empty (info \| search),` `existence (info \| search),` `square (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP825

Ticks mark an infinite sequence of angles on circle such that each angle is the double of the subsequent angle in the sequence (angle measured from rightmost indicated point) vs. not so.

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	COMMENTS	`This is solvable; it was solved by Sridhar Ramesh.` `A full turn is considered "the same angle" as no turns; likewise for adding and subtracting full turns from any angle. All sequences of angles shown start at the rightmost tick.` `It doesn't matter whether the angle is measured clockwise or counterclockwise, as long as the choice is consistent.`
	CROSSREFS	`Adjacent-numbered pages: BP820 BP821 BP822 BP823 BP824 * BP826 BP827 BP828 BP829 BP830`
	KEYWORD	`hard, convoluted, notso, math, solved`
	CONCEPT	`sequence (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP365

Two independent quantities changing simultaneously vs. determined by just one changing quantity.

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	COMMENTS	`Examples sorted right may feature multiple quantities, but one changing quantity determines all changing quantities.` `The distinction between the two sides is fuzzy. For example the left-sorted example EX4364 could be viewed as determined by just the one changing quantity of width and the fact that the height is given by two times the width minus one. On the other hand the right-sorted example EX4370 could be viewed as determined by the two changing quantities number of black squares and number of white squares, ignoring the fact that the total number of squares is always six.`
	CROSSREFS	`Adjacent-numbered pages: BP360 BP361 BP362 BP363 BP364 * BP366 BP367 BP368 BP369 BP370`
	KEYWORD	`fuzzy, traditional, rules, miniworlds`
	CONCEPT	`size_increase_decrease (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP63

Shading thicker on the right side vs. shading thicker on the left side.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 234.`
	CROSSREFS	`Adjacent-numbered pages: BP58 BP59 BP60 BP61 BP62 * BP64 BP65 BP66 BP67 BP68`
	KEYWORD	`dual, handed, finished, traditional, viceversa, bongard`
	CONCEPT	`left_right (info \| search),` `curve_texture (info \| search),` `texture (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

BP290

If any non-nosed faces exist, they are happy if and only if happy nosed faces exist as well vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP285 BP286 BP287 BP288 BP289 * BP291 BP292 BP293 BP294 BP295`
	KEYWORD	`convoluted`
	CONCEPT	`existence (info \| search),` `iff (info \| search)`
	AUTHOR	`"Lewis"`

BP307

Dots are in tight clusters around convex vertices vs. dots are spread around.

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	CROSSREFS	`BP308 is similar.` `Adjacent-numbered pages: BP302 BP303 BP304 BP305 BP306 * BP308 BP309 BP310 BP311 BP312`
	KEYWORD	`traditional`
	CONCEPT	`vertex_of_meeting_lines (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search)`
	AUTHOR	`"Lewis"`

BP162

Every other side, if extended, passes through one point vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP157 BP158 BP159 BP160 BP161 * BP163 BP164 BP165 BP166 BP167`
	KEYWORD	`hard, noisy, traditional`
	CONCEPT	`lines_coincide (info \| search),` `every_other (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP167

Every cluster has two clusters of dots vs. every cluster has three clusters of dots.

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	CROSSREFS	`Adjacent-numbered pages: BP162 BP163 BP164 BP165 BP166 * BP168 BP169 BP170 BP171 BP172`
	KEYWORD	`traditional`
	CONCEPT	`number (info \| search),` `dot (info \| search),` `recursion (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`Multiple options: dot_clusters [smaller \| same \| bigger], point_clusters [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP1071

Two of the same kind within in one region vs. not so.

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	CROSSREFS	`See BP977 for a version without infinite nesting and other drawings than boxes.` `Adjacent-numbered pages: BP1066 BP1067 BP1068 BP1069 BP1070 * BP1072 BP1073 BP1074 BP1075 BP1076`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP378

The two objects are conceptually related vs. the two objects are conceptually unrelated.

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	CROSSREFS	`See BP347, which is similar.` `Adjacent-numbered pages: BP373 BP374 BP375 BP376 BP377 * BP379 BP380 BP381 BP382 BP383`
	KEYWORD	`abstract, math, unorderedpair, traditional`
	CONCEPT	`same_concept (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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