The On-Line Encyclopedia of Bongard Problems

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Counterclockwise along the curve following the arrow vs. clockwise along the curve following the arrow.

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

	CROSSREFS	`Adjacent-numbered pages: BP358 BP359 BP360 BP361 BP362 * BP364 BP365 BP366 BP367 BP368`
	KEYWORD	`easy, nice, dual, handed, leftright, updown, gap, traditional`
	CONCEPT	`arrow (info \| search),` `turn_orientation (info \| search),` `tracing_line_or_curve (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Quadrilateral that is nearly a triangle vs. typical quadrilateral.

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

	CROSSREFS	`Adjacent-numbered pages: BP155 BP156 BP157 BP158 BP159 * BP161 BP162 BP163 BP164 BP165`
	KEYWORD	`perfect, traditional`
	CONCEPT	`imperfection_small (info \| search),` `number (info \| search),` `triangle (info \| search)`
	WORLD	`Multiple options: [smaller \| same \| bigger], quadrilateral_outline [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

Equal horizontal length vs. not

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

	COMMENTS	`All examples in this Problem are pairs of straight line segments.` `This problem communicates the idea of projected distance, in this case from 2D to 1D (x-axis).`
	CROSSREFS	`Adjacent-numbered pages: BP552 BP553 BP554 BP555 BP556 * BP558 BP559 BP560 BP561 BP562`
	KEYWORD	`nice, precise, allsorted, stretch, perfect, unorderedpair, preciseworld`
	CONCEPT	`projection (info \| search)`
	WORLD	`two_segments [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

Number of objects is one less than sides of each object vs. number of objects is one more than sides of each object.

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

	CROSSREFS	`Adjacent-numbered pages: BP159 BP160 BP161 BP162 BP163 * BP165 BP166 BP167 BP168 BP169`
	KEYWORD	`nice, traditional`
	CONCEPT	`subtraction (info \| search),` `number (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

Any symmetry exhibited by some non-empty subset of the objects is also a symmetry of the whole thing vs. not so.

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

	COMMENTS	`In other words, placing the image over itself (rotation and flipping allowed) so that any parts match up makes the whole image match up to itself vs. not so.`
	CROSSREFS	`See BP965 for a variation on this idea where the "parts" are allowed to be arbitrary regions of the image instead of individual objects shown in the image.` `Adjacent-numbered pages: BP1241 BP1242 BP1243 BP1244 BP1245 * BP1247 BP1248 BP1249 BP1250 BP1251`
	KEYWORD	`precise, allsorted, unwordable, notso, traditional`
	CONCEPT	`local_global (info \| search),` `self-reference (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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

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

	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`

Number of enclosed black circles varies in correlation with enclosing circle outline size vs. not so.

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

	COMMENTS	`This is a Bongard Problem about comparing something discrete (number) with something continuous (size).` `The inner black circles vary in size randomly. (This forces the solution to be about the discrete number of black circles instead of their combined area.)`
	CROSSREFS	`Adjacent-numbered pages: BP312 BP313 BP314 BP315 BP316 * BP318 BP319 BP320 BP321 BP322`
	KEYWORD	`nice, traditional`
	CONCEPT	`inside (info \| search),` `dot (info \| search),` `proportional (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

There is no rule for how the objects in a cluster interrelate vs. there is.

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

	COMMENTS	`Other ways of phrasing this:` `"Local" vs. "global" properties of collections: to check a collection satisfies a "local" property, it is only necessary to check each individual thing in it satisfies some property.` `The rule all collections satisfy is just "every object is a ___" vs. the rule is something more.`
	CROSSREFS	`Adjacent-numbered pages: BP1122 BP1123 BP1124 BP1125 BP1126 * BP1128 BP1129 BP1130 BP1131 BP1132`
	KEYWORD	`abstract, creativeexamples, left-unknowable, rules, miniworlds`
	CONCEPT	`local_global (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Small object can glide in the bay vs. small object cannot glide in the bay.

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

	CROSSREFS	`Adjacent-numbered pages: BP170 BP171 BP172 BP173 BP174 * BP176 BP177 BP178 BP179 BP180`
	KEYWORD	`orderedpair, traditional`
	CONCEPT	`entrance_exit (info \| search),` `indentation (info \| search),` `rotation_required (info \| search),` `imagined_motion (info \| search),` `motion (info \| search),` `specific_shape (info \| search),` `physically_fitting (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Nodes share the same edge connections as the vertices of a cube vs. not so.

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

	REFERENCE	`https://mathworld.wolfram.com/CubicalGraph.html`
	CROSSREFS	`Adjacent-numbered pages: BP1097 BP1098 BP1099 BP1100 BP1101 * BP1103 BP1104 BP1105 BP1106 BP1107`
	KEYWORD	`precise, allsorted, arbitrary, help, preciseworld`
	CONCEPT	`graph (info \| search),` `cube (info \| search),` `distinguishing_crossing_curves (info \| search),` `topological_transformation (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

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