The On-Line Encyclopedia of Bongard Problems

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Any one gear turns all vs. no gear turns all.

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	CROSSREFS	`See BP536 for all gears can turn.` `Adjacent-numbered pages: BP331 BP332 BP333 BP334 BP335 * BP337 BP338 BP339 BP340 BP341`
	KEYWORD	`nice, stretch, physics, traditional`
	CONCEPT	`all (info \| search),` `turn_orientation (info \| search),` `every_other (info \| search),` `gear (info \| search),` `on_line_or_curve (info \| search),` `tracing_line_or_curve (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	WORLD	`gears [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

There is a point that can see (in straight lines) all points vs. there is no point that can see (in straight lines) all points.

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	COMMENTS	`Left examples are called "star domains."`
	CROSSREFS	`See BP388 for whether a distinguished point can see all points.` `Adjacent-numbered pages: BP363 BP364 BP365 BP366 BP367 * BP369 BP370 BP371 BP372 BP373`
	KEYWORD	`nice, precise, unstable, perfect, traditional`
	CONCEPT	`all (info \| search),` `existence (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`shape [smaller \| same \| bigger] zoom in left (fill_shape_with_seeing_point)`
	AUTHOR	`Aaron David Fairbanks`

A "chess piece" that moves as shown may reach every square vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP371 BP372 BP373 BP374 BP375 * BP377 BP378 BP379 BP380 BP381`
	KEYWORD	`precise, allsorted, notso, left-finite, right-finite, traditional, fixedgrid, preciseworld`
	CONCEPT	`all (info \| search),` `chess-like (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

White dot can see (in straight lines) all black points vs. white dot cannot see (in straight lines) all black points.

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	CROSSREFS	`See BP368 for whether ALL points can see all points.` `Adjacent-numbered pages: BP383 BP384 BP385 BP386 BP387 * BP389 BP390 BP391 BP392 BP393`
	KEYWORD	`nice, traditional`
	CONCEPT	`all (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	WORLD	`fill_shape_white_dot [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

All gears can make complete turns vs. not so.

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	CROSSREFS	`See BP336 for one gear turns all.` `Adjacent-numbered pages: BP531 BP532 BP533 BP534 BP535 * BP537 BP538 BP539 BP540 BP541`
	KEYWORD	`stretch, physics, traditional`
	CONCEPT	`all (info \| search),` `gear (info \| search)`
	WORLD	`gears [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

There exists a closed trail that hits each edge exactly once vs. not so.

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	COMMENTS	`Left examples are called "Eulerian graphs."` `A connected graph is Eulerian if and only if each vertex is incident to an even number of edges.`
	CROSSREFS	`Adjacent-numbered pages: BP555 BP556 BP557 BP558 BP559 * BP561 BP562 BP563 BP564 BP565`
	KEYWORD	`precise, allsorted, math, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `all (info \| search),` `even_odd (info \| search),` `existence (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Polygons where all sides are different lengths vs. Polygons where not all sides are different lengths.

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	COMMENTS	`All examples in this Problem are outlines of convex polygons.` `This is a generalisation of scalene triangles to any polygon.`
	CROSSREFS	`The left side implies the right side of BP329 (regular vs. irregular polygons), but the converse is not true.` `The left side of BP329 implies the right side, but the converse is not true.` `Adjacent-numbered pages: BP919 BP920 BP921 BP922 BP923 * BP925 BP926 BP927 BP928 BP929`
	EXAMPLE	`Any scalene triangle will fit on the left, because no two sides are equal.` `However, any regular polygon will not fit on the left, because all of its sides are equal.` `A random convex polygon will "almost surely" fit on the left.`
	KEYWORD	`nice, stretch, right-narrow, traditional`
	CONCEPT	`all (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

Every vertex is connected to every other vs. vertices are connected in a cycle (no other connections).

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	COMMENTS	`Complete graphs with zero, one, two, or three vertices would be ambiguously categorized (fit in overlap of both sides).` `Left examples are called "fully connected graphs." Right examples are called "cycle graphs."`
	CROSSREFS	`Adjacent-numbered pages: BP927 BP928 BP929 BP930 BP931 * BP933 BP934 BP935 BP936 BP937`
	KEYWORD	`precise, left-narrow, right-narrow, both, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `all (info \| search),` `loop (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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`

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