The On-Line Encyclopedia of Bongard Problems

Search: author:Leo Crabbe

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BP1146

Same number of dots in top row as in leftmost column vs not so.

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	COMMENTS	`This is a difficult-to-read attempt at making a Bongard Problem about perfect numbers. Grouping columns together to make rectangular arrays, each maximal (most dots possible) rectangular array of a particular height in any given example has the same number of dots in it (a perfect number, in left-sorted cases), and the dot-width of each array represents a particular divisor of that number.` `It is not currently known whether there are a finite amount of examples that would be sorted left.` `Every example in this Bongard Problem corresponds to a distinct natural number. There is not a way of representing the number 1 using the rules of construction for examples in this problem (if the problem were simply "Perfect number of dots vs. other number of dots", the example with 1 dot would be sorted right).`
	REFERENCE	`https://en.wikipedia.org/wiki/Perfect_number`
	CROSSREFS	`Adjacent-numbered pages: BP1141 BP1142 BP1143 BP1144 BP1145 * BP1147 BP1148 BP1149 BP1150 BP1151`
	KEYWORD	`overriddensolution, left-listable, right-listable`
	AUTHOR	`Leo Crabbe`

BP1145

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`

BP1141

Object inside of bounding box vs. object outside of bounding box.

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	COMMENTS	`This Problem is not to be taken seriously.`
	CROSSREFS	`Adjacent-numbered pages: BP1136 BP1137 BP1138 BP1139 BP1140 * BP1142 BP1143 BP1144 BP1145 BP1146`
	KEYWORD	`example, overriddensolution, right-full, right-null, invalid, experimental, funny`
	AUTHOR	`Leo Crabbe`

BP1136

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`

BP1135

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`

BP1133

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`

BP1132

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`

BP1131

One shape can be totally obscured by the other vs. neither shape can be obscured.

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	COMMENTS	`Rotation of shapes is not required for any left-hand panels, but it should not change any example's sorting if it is considered.`
	CROSSREFS	`Adjacent-numbered pages: BP1126 BP1127 BP1128 BP1129 BP1130 * BP1132 BP1133 BP1134 BP1135 BP1136`
	KEYWORD	`nice, precise, allsorted, pixelperfect, unorderedpair`
	CONCEPT	`overlap (info \| search)`
	WORLD	`2_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1122

Content of any square is an image of the whole panel vs. not so.

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

	CROSSREFS	`Similar to BP818.` `Adjacent-numbered pages: BP1117 BP1118 BP1119 BP1120 BP1121 * BP1123 BP1124 BP1125 BP1126 BP1127`
	KEYWORD	`nice, minimal, size, boundingbox, infinitedetail, preciseworld, absoluteposition`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1110

The process that turns one object into the other is the same both ways vs. the process changes depending on which object is chosen as the starting point.

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

	REFERENCE	`https://en.wikipedia.org/wiki/Duality_(mathematics)` `https://en.wikipedia.org/wiki/Involution_(mathematics)`
	CROSSREFS	`This is a special case of BP841 and a generalisation of BP822.` `Adjacent-numbered pages: BP1105 BP1106 BP1107 BP1108 BP1109 * BP1111 BP1112 BP1113 BP1114 BP1115`
	KEYWORD	`nice, abstract, math, anticomputer, creativeexamples, left-narrow, unorderedpair, rules, miniworlds, dithering`
	CONCEPT	`function (info \| search)`
	AUTHOR	`Leo Crabbe`

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