The On-Line Encyclopedia of Bongard Problems

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Meta Bongard Problems that can contain an infinite chain of Bongard Problems containing Bongard Problems vs. this can never happen.

BP794

BP1073

BP552	BP553	BP554	BP556	BP567	BP572
BP838	BP913	BP958	BP976	BP995	BP1079
BP1081

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

	COMMENTS	`Right examples have the keyword "wellfounded" on the OEBP.` `This BP is not wellfounded, but its right side is. A paradoxical BP would be "Meta Bongard Problems that can contain an infinite chain of Bongard Problems containing Bongard Problems on the right side vs. this can never happen": where does it sort itself?`
	CROSSREFS	`left-self or right-self implies not wellfounded.` `Wellfounded implies not feedback.` `Adjacent-numbered pages: BP789 BP790 BP791 BP792 BP793 * BP795 BP796 BP797 BP798 BP799`
	KEYWORD	`meta (see left/right), links, keyword, left-self, metameta, left-it, feedback`
	CONCEPT	`recursion (info \| search)`
	WORLD	`linksbp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

All interiors are convex vs. at least one concave interior.

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

	CROSSREFS	`Adjacent-numbered pages: BP172 BP173 BP174 BP175 BP176 * BP178 BP179 BP180 BP181 BP182`
	KEYWORD	`traditional`
	CONCEPT	`all (info \| search),` `concave_convex_angle (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Innermost shape is reachable from the outermost one vs. innermost shape is unreachable from the outermost one.

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

	CROSSREFS	`Adjacent-numbered pages: BP110 BP111 BP112 BP113 BP114 * BP116 BP117 BP118 BP119 BP120`
	KEYWORD	`traditional`
	CONCEPT	`innermost_outermost (info \| search),` `path (info \| search),` `reachable (info \| search),` `tracing_line_or_curve (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

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

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

	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`

Bulky interior, if closed vs. narrow interior, if closed.

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

	CROSSREFS	`Adjacent-numbered pages: BP163 BP164 BP165 BP166 BP167 * BP169 BP170 BP171 BP172 BP173`
	KEYWORD	`traditional`
	CONCEPT	`elongated_compact (info \| search),` `imperfection_small (info \| search)`
	AUTHOR	`Harry E. Foundalis`

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`

Some quantity keeps increasing from left to right vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP345 BP346 BP347 BP348 BP349 * BP351 BP352 BP353 BP354 BP355`
	KEYWORD	`creativeexamples, structure, sequence, traditional, rules`
	CONCEPT	`size_increase_decrease (info \| search),` `iteration (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`quantity_vary_seq_noise_allowed [smaller \| same \| bigger] zoom in left (quantity_change_seq_increase_right_noise_allowed)`
	AUTHOR	`Aaron David Fairbanks`

Prime knot vs. composite knot.

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	REFERENCE	`https://en.wikipedia.org/wiki/Prime_knot`
	CROSSREFS	`Adjacent-numbered pages: BP848 BP849 BP850 BP851 BP852 * BP854 BP855 BP856 BP857 BP858`
	KEYWORD	`math, hardsort`
	CONCEPT	`knot (info \| search)`
	WORLD	`knot [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

No axis of symmetry vs. vertical axis of symmetry.

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

	CROSSREFS	`BP50 is the same solution (with the sides switched), using multiple shapes and with some shapes filled in black.` `BP1206 is like BP50 but instead of "no axis of symmetry at all" it uses "no vertical axis of symmetry".` `Adjacent-numbered pages: BP147 BP148 BP149 BP150 BP151 * BP153 BP154 BP155 BP156 BP157`
	KEYWORD	`rotate, stretch, traditional`
	CONCEPT	`existence (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Regular star polygon vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP335 BP336 BP337 BP338 BP339 * BP341 BP342 BP343 BP344 BP345`
	KEYWORD	`math, traditional`
	CONCEPT	`tracing_line_or_curve (info \| search),` `vertex_of_meeting_lines (info \| search),` `write_in_single_stroke (info \| search)`
	WORLD	`figure_made_of_segments [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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