The On-Line Encyclopedia of Bongard Problems

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BP937

Shapes have equal perimeter vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP932 BP933 BP934 BP935 BP936 * BP938 BP939 BP940 BP941 BP942`
	KEYWORD	`precise, allsorted, unstable, left-narrow, perfect, unorderedpair`
	CONCEPT	`perimeter (info \| search)`
	WORLD	`2_fill_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP969

Triangle is smallest black shape vs. square is smallest black shape.

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

	CROSSREFS	`Adjacent-numbered pages: BP964 BP965 BP966 BP967 BP968 * BP970 BP971 BP972 BP973 BP974`
	KEYWORD	`stub`
	CONCEPT	`size (info \| search),` `square (info \| search),` `triangle (info \| search),` `most (info \| search),` `quantity_comparison (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP977

Two of the same object are enclosed in the same space (there is a path between them) vs. not so.

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	COMMENTS	`An "object" is everything within some black boundary.`
	CROSSREFS	`See BP1071 for a version with only squares and with infinite nesting allowed.` `Adjacent-numbered pages: BP972 BP973 BP974 BP975 BP976 * BP978 BP979 BP980 BP981 BP982`
	KEYWORD	`nice, precise, allsorted, creativeexamples, traditional`
	CONCEPT	`separated_regions (info \| search),` `identical (info \| search),` `recursion (info \| search),` `imagined_line_or_curve (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP986

Palindromes vs. not palindromes.

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	COMMENTS	`All examples in this Problem are sequences of graphic symbols. In this Problem, a "palindrome" is taken to be an ordered sequence which is the same read left-to-right as it is read right-to-left. A more formal solution to this Problem could be: "Sequences which are invariant under a permutation which swaps first and last entries, second and second last entries, third and third last entries, ... and so on vs. sequences which are not invariant under the aforementioned permutamation."`
	CROSSREFS	`Adjacent-numbered pages: BP981 BP982 BP983 BP984 BP985 * BP987 BP988 BP989 BP990 BP991`
	KEYWORD	`nice, precise, allsorted, notso, sequence, traditional`
	CONCEPT	`element_wise_symmetry (info \| search),` `identical (info \| search),` `sequence (info \| search),` `same_shape (info \| search),` `same (info \| search),` `symmetry (info \| search)`
	WORLD	`zoom in left \| zoom in right`
	AUTHOR	`Jago Collins`

BP1016

Rigid vs. not rigid.

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	REFERENCE	`Henneberg, L. (1911), Die graphische Statik der starren Systeme, Leipzig` `Jackson, Bill. (2007). Notes on the Rigidity of Graphs.` `Laman, Gerard. (1970), "On graphs and the rigidity of plane skeletal structures", J. Engineering Mathematics, 4 (4): 331–340.` `Pollaczek‐Geiringer, Hilda (1927), "Über die Gliederung ebener Fachwerke", Zeitschrift für Angewandte Mathematik und Mechanik, 7 (1): 58–72.`
	CROSSREFS	`Adjacent-numbered pages: BP1011 BP1012 BP1013 BP1014 BP1015 * BP1017 BP1018 BP1019 BP1020 BP1021`
	KEYWORD	`nice, physics, help`
	CONCEPT	`rigidity (info \| search),` `graph (info \| search),` `imagined_motion (info \| search)`
	WORLD	`planar_connected_graph [smaller \| same \| bigger] zoom in left (rigid_planar_connected_graph)`
	AUTHOR	`Aaron David Fairbanks`

BP1099

Considering only the ways they are connected, anything that can be said about a given node can be said about every other node vs. not so.

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	REFERENCE	`https://en.wikipedia.org/wiki/Vertex-transitive_graph`
	CROSSREFS	`Adjacent-numbered pages: BP1094 BP1095 BP1096 BP1097 BP1098 * BP1100 BP1101 BP1102 BP1103 BP1104`
	KEYWORD	`precise, allsorted, notso, math, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`graph [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP1100

There is a path between any two nodes vs. not so.

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	REFERENCE	`https://en.wikipedia.org/wiki/Graph_theory` `https://en.wikipedia.org/wiki/Connectivity_(graph_theory)`
	CROSSREFS	`Adjacent-numbered pages: BP1095 BP1096 BP1097 BP1098 BP1099 * BP1101 BP1102 BP1103 BP1104 BP1105`
	KEYWORD	`precise, allsorted, world, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `connected_component (info \| search)`
	WORLD	`graph [smaller \| same \| bigger] zoom in left (connected_graph) \| zoom in right (disconnected_graph)`
	AUTHOR	`Leo Crabbe`

BP1101

Each node is connected to the same number of nodes by straight lines vs. not so.

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

	REFERENCE	`https://en.wikipedia.org/wiki/Regular_graph`
	CROSSREFS	`Any left example of BP1099 will be a left example for this BP.` `Adjacent-numbered pages: BP1096 BP1097 BP1098 BP1099 BP1100 * BP1102 BP1103 BP1104 BP1105 BP1106`
	KEYWORD	`precise, allsorted, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`graph [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Leo Crabbe`

BP1109

Considering only the ways they are connected, anything that can be said about a given edge can be said about every other edge vs. not so.

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

	REFERENCE	`https://mathworld.wolfram.com/Edge-TransitiveGraph.html`
	CROSSREFS	`Adjacent-numbered pages: BP1104 BP1105 BP1106 BP1107 BP1108 * BP1110 BP1111 BP1112 BP1113 BP1114`
	KEYWORD	`precise, allsorted, notso, math, left-narrow, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`graph [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

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