The On-Line Encyclopedia of Bongard Problems

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Circle that passes through points is contained within bounding box vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1127 BP1128 BP1129 BP1130 BP1131 * BP1133 BP1134 BP1135 BP1136 BP1137`
	KEYWORD	`precise, allsorted, boundingbox, hardsort, preciseworld, absoluteposition`
	CONCEPT	`circle (info \| search),` `imagined_entity (info \| search)`
	WORLD	`three_points [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

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`

Each component can be assigned its own layer in the arrangement vs. there is no equivalent way of dividing the arrangement into layers.

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	COMMENTS	`Put differently, if the examples are imagined to be arrangements of rigid sticks/hoops/etc resting on a flat surface, positive examples include sticks/hoops/etc that could be picked up without disturbing the other objects.`
	CROSSREFS	`Adjacent-numbered pages: BP1130 BP1131 BP1132 BP1133 BP1134 * BP1136 BP1137 BP1138 BP1139 BP1140`
	KEYWORD	`precise`
	AUTHOR	`Leo Crabbe`

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`

Constructible Polygon vs. Non-constructible Polygon

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	REFERENCE	`https://en.wikipedia.org/wiki/Straightedge_and_compass_construction` `https://en.wikipedia.org/wiki/Constructible_polygon`
	CROSSREFS	`Adjacent-numbered pages: BP1132 BP1133 BP1134 BP1135 BP1136 * BP1138 BP1139 BP1140 BP1141 BP1142`
	KEYWORD	`stub, precise, math, hardsort, proofsrequired, preciseworld`
	AUTHOR	`Jago Collins`

Each attribute is shared by every group or none vs. some attribute is shared by exactly two groups

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	COMMENTS	`Attributes are shading, shape, and number.` `There are always three groups.` `This problem is related to the card game Set.`
	CROSSREFS	`Adjacent-numbered pages: BP1133 BP1134 BP1135 BP1136 BP1137 * BP1139 BP1140 BP1141 BP1142 BP1143`
	KEYWORD	`nice, precise, allsorted, notso, preciseworld`
	CONCEPT	`all (info \| search),` `number (info \| search),` `same (info \| search),` `two (info \| search),` `three (info \| search)`
	AUTHOR	`William B Holland`

Polygon that can be achieved by folding a square once vs. other polygons.

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	COMMENTS	`Although it is tempting at first to make a version of this Bongard Problem with the solution "Shape can be achieved by folding a square a finite amount of times vs. other shapes", this alternate Bongard Problem would just amount to having the solution "Convex shape with straight edges vs. concave shape or convex shape with at least one curved edge."`
	CROSSREFS	`Adjacent-numbered pages: BP1140 BP1141 BP1142 BP1143 BP1144 * BP1146 BP1147 BP1148 BP1149 BP1150`
	KEYWORD	`precise, notso, stretch, left-narrow, finishedexamples, preciseworld`
	CONCEPT	`square (info \| search)`
	AUTHOR	`Leo Crabbe`

Columns of the table could be respectively labeled "Number" and "Number of times number appears in this table" vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1142 BP1143 BP1144 BP1145 BP1146 * BP1148 BP1149 BP1150 BP1151 BP1152`
	KEYWORD	`nice, precise, notso, handed, leftright, left-narrow, grid, preciseworld, left-listable, right-listable`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

Number of dots in the Nth box (from the left) is how many times the number (N - 1) appears in the whole diagram vs. not so.

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	COMMENTS	`Left-sorted examples are sometimes called autobiographical or self-descriptive numbers.`
	REFERENCE	`https://oeis.org/A349595` `https://en.wikipedia.org/wiki/Self-descriptive_number`
	CROSSREFS	`See BP1147 for a similar idea.` `BP1149 was inspired by this.` `Adjacent-numbered pages: BP1143 BP1144 BP1145 BP1146 BP1147 * BP1149 BP1150 BP1151 BP1152 BP1153`
	KEYWORD	`nice, precise, unwordable, notso, handed, leftright, left-narrow, sequence, preciseworld, left-listable, right-listable`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

Number in the Nth box (from the left) is how many numbers appear N times vs. not so.

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	CROSSREFS	`Inspired by BP1148.` `Adjacent-numbered pages: BP1144 BP1145 BP1146 BP1147 BP1148 * BP1150 BP1151 BP1152 BP1153 BP1154`
	KEYWORD	`nice, precise, unwordable, notso, handed, leftright, left-narrow, sequence, preciseworld, left-listable, right-listable`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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