The On-Line Encyclopedia of Bongard Problems

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Regions in drawing (ignore background) can be coloured using three or fewer colours such that no adjacent regions are coloured the same colour vs. four colours are required.

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

	COMMENTS	`This Problem is related to the four colour theorem.`
	CROSSREFS	`Adjacent-numbered pages: BP894 BP895 BP896 BP897 BP898 * BP900 BP901 BP902 BP903 BP904`
	KEYWORD	`hard, nice, math`
	CONCEPT	`separated_regions (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP900

Black shape is a valid shadow (2D projection) of 3D shape vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP895 BP896 BP897 BP898 BP899 * BP901 BP902 BP903 BP904 BP905`
	KEYWORD	`3d, orderedpair`
	CONCEPT	`3d_solid (info \| search),` `projection (info \| search)`
	AUTHOR	`Leo Crabbe`

BP901

Bongard Problem with solution relating to concept: projection of an object onto a lower dimension vs. Bongard Problem unrelated to this concept.

BP557

BP900

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

	CROSSREFS	`Adjacent-numbered pages: BP896 BP897 BP898 BP899 BP900 * BP902 BP903 BP904 BP905 BP906`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "projection"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP902

This Bongard Problem vs. anything else.

BP902

BP1

becious

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

	COMMENTS	`Although this Bongard Problem is self-referential, it's only because of the specific phrasing of the solution. "BP902 vs. anything else" would also work. The number 902 could have been chosen coincidentally.`
	CROSSREFS	`See BP953, BP959.` `Adjacent-numbered pages: BP897 BP898 BP899 BP900 BP901 * BP903 BP904 BP905 BP906 BP907`
	KEYWORD	`notso, meta (see left/right), links, left-self, left-narrow, left-finite, left-full, right-null, right-it, invalid, experimental, funny`
	CONCEPT	`self-reference (info \| search),` `specificity (info \| search)`
	WORLD	`everything [smaller \| same] zoom in left (bp902)`
	AUTHOR	`Leo Crabbe`

BP903

Sharp vs. blurry

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

	CROSSREFS	`Adjacent-numbered pages: BP898 BP899 BP900 BP901 BP902 * BP904 BP905 BP906 BP907 BP908`
	KEYWORD	`contributepairs`
	CONCEPT	`contrast (info \| search),` `curve_texture (info \| search)`
	AUTHOR	`Cameron Fetter`

BP904

Rows show all possible ways a certain number of dots can be divided between a certain number of bins vs. not so.

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

	COMMENTS	`The rows in the panels on the right hand side show all the ways you can divide a certain number of dots between a certain number of bins, ignoring which bins they are placed in.`
	CROSSREFS	`Adjacent-numbered pages: BP899 BP900 BP901 BP902 BP903 * BP905 BP906 BP907 BP908 BP909`
	KEYWORD	`solved, left-null, grid, left-listable, right-listable`
	CONCEPT	`permutation (info \| search)`
	AUTHOR	`Molly C Klenzak`

BP905

Graph can be redrawn such that no edges intersect vs. not so.

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

	COMMENTS	`A graph is a collection of vertices and edges. Vertices are the dots and edges are the lines that connect the dots. On the left, all edges can be redrawn (curved lines are allowed and moving vertices is allowed) such that no edges cross each other and each vertex is still connected to the same other vertices. These graphs are called planar.`
	CROSSREFS	`Adjacent-numbered pages: BP900 BP901 BP902 BP903 BP904 * BP906 BP907 BP908 BP909 BP910`
	KEYWORD	`nice, precise, allsorted, notso, math, left-null, preciseworld`
	CONCEPT	`graph (info \| search),` `topological_transformation (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Molly C Klenzak`

BP906

Bongard Problem with solution relating to concept: 2 inputs 1 output vs. Bongard Problem unrelated to this concept.

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

	CROSSREFS	`Adjacent-numbered pages: BP901 BP902 BP903 BP904 BP905 * BP907 BP908 BP909 BP910 BP911`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "2_inputs_1_output"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP907

One dot cluster is the product of the other two vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP902 BP903 BP904 BP905 BP906 * BP908 BP909 BP910 BP911 BP912`
	KEYWORD	`unorderedtriplet`
	CONCEPT	`2_inputs_1_output (info \| search),` `product (info \| search)`
	WORLD	`3_dot_clusters [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP908

Ordered triplet comparison Bongard Problems vs. unordered triplet comparison Bongard Problems

	BP54	BP64	BP234	BP324	BP325	BP339
	BP381	BP548	BP558	BP790	BP791	BP1260

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

	COMMENTS	`Left examples have the keyword "orderedtriplet" on the OEBP.` `Right examples have the keyword "unorderedtriplet" on the OEBP.` `An ordered triplet can be totally ordered (swapping any 2 objects would change the information being conveyed by the panel) or partially ordered (unordered pair and a 3rd object that relates to the pair).`
	CROSSREFS	`Adjacent-numbered pages: BP903 BP904 BP905 BP906 BP907 * BP909 BP910 BP911 BP912 BP913`
	KEYWORD	`meta (see left/right), links, keyword`
	WORLD	`triplet_comparison_bp [smaller \| same \| bigger] zoom in left (ordered_triplet_comparison_bp)`
	AUTHOR	`Leo Crabbe`

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