The On-Line Encyclopedia of Bongard Problems

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Shape can be combined with a copy of itself to form a convex shape vs. not so.

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	CROSSREFS	`For the generalization of this property, see BP991.` `Adjacent-numbered pages: BP815 BP816 BP817 BP818 BP819 * BP821 BP822 BP823 BP824 BP825`
	KEYWORD	`nice, precise, allsorted`
	CONCEPT	`tiling (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger] zoom in left`
	AUTHOR	`Isaac Hathaway`

BP850

Shape can be maneuvered around the corner vs. not so.

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

	REFERENCE	`https://en.wikipedia.org/wiki/Moving_sofa_problem`
	CROSSREFS	`Adjacent-numbered pages: BP845 BP846 BP847 BP848 BP849 * BP851 BP852 BP853 BP854 BP855`
	KEYWORD	`nice, precise, physics, creativeexamples, proofsrequired, left-narrow, right-narrow, dithering`
	CONCEPT	`rotation_required (info \| search),` `imagined_motion (info \| search),` `physically_fitting (info \| search)`
	AUTHOR	`Leo Crabbe`

BP856

Compound shape would hit the dot if rotated vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP851 BP852 BP853 BP854 BP855 * BP857 BP858 BP859 BP860 BP861`
	KEYWORD	`nice, precise, allsorted, left-narrow, preciseworld`
	CONCEPT	`imagined_motion (info \| search),` `collision (info \| search)`
	AUTHOR	`Leo Crabbe`

BP860

Finitely many copies of the shape can be arranged such that they are locked together vs. not so.

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

	CROSSREFS	`This is a generalisation of BP861.` `Adjacent-numbered pages: BP855 BP856 BP857 BP858 BP859 * BP861 BP862 BP863 BP864 BP865`
	KEYWORD	`hard, nice, stub, precise, stretch, unstable, hardsort, challenge, creativeexamples, perfect, pixelperfect`
	CONCEPT	`tiling (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP861

Shape can be combined with a copy of itself such that they are locked together vs. not so.

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

	CROSSREFS	`See BP860 for the more general version of this solution.` `Adjacent-numbered pages: BP856 BP857 BP858 BP859 BP860 * BP862 BP863 BP864 BP865 BP866`
	KEYWORD	`nice, precise, unstable, perfect, pixelperfect`
	CONCEPT	`tiling (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP863

Two shapes can tessellate the plane together vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP858 BP859 BP860 BP861 BP862 * BP864 BP865 BP866 BP867 BP868`
	KEYWORD	`nice, precise, allsorted, math, hardsort, creativeexamples, unorderedpair`
	CONCEPT	`infinite_plane (info \| search),` `tessellation (info \| search),` `tiling (info \| search)`
	WORLD	`2_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP891

Dots can be connected to create one triangle within another vs. not so.

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	COMMENTS	`Or equivalently, "3 dots on boundary of convex hull vs. not so". - Leo Crabbe, Aug 01 2020`
	CROSSREFS	`Adjacent-numbered pages: BP886 BP887 BP888 BP889 BP890 * BP892 BP893 BP894 BP895 BP896`
	KEYWORD	`nice, precise, allsorted, preciseworld`
	CONCEPT	`convex_hull (info \| search),` `triangle (info \| search)`
	WORLD	`6_dots [smaller \| same \| bigger]`
	AUTHOR	`Cameron Fetter`

BP892

Black shapes can be arranged such that they fit inside rectangular outline vs. not so.

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	COMMENTS	`There is a slight ambiguity here regarding whether a shape could be placed within another shape's hole. This is a question of how one perceives the Problem: are we sliding shapes around on a table in 2D or are we allowed to 'lift' them in 3D space?`
	CROSSREFS	`Adjacent-numbered pages: BP887 BP888 BP889 BP890 BP891 * BP893 BP894 BP895 BP896 BP897`
	KEYWORD	`nice, precise, perfect, pixelperfect, help`
	CONCEPT	`rotation_required (info \| search),` `physically_fitting (info \| search)`
	AUTHOR	`Leo Crabbe`

BP897

Wide angles connected to narrow angles vs. not so.

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

	COMMENTS	`Another way to phrase this solution is that right examples can be folded down flat onto one isosceles triangle while left examples cannot.` `All examples in this Problem feature four isosceles triangles connected by corners and/or edges.`
	CROSSREFS	`This was conceived as a false solution for BP898.` `Adjacent-numbered pages: BP892 BP893 BP894 BP895 BP896 * BP898 BP899 BP900 BP901 BP902`
	KEYWORD	`nice, precise, allsorted, notso, traditional, preciseworld`
	CONCEPT	`triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Molly C Klenzak, Aaron David Fairbanks`

BP898

Can fold into tetragonal disphenoid ("isosceles tetrahedron") vs. cannot.

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	COMMENTS	`Which two sides are the long sides and which side is the short side, or equivalently which angles are the wider angles and which angle is the narrower angle, is the only relevant information to consider for each triangle. Triangles are all assumed isosceles and congruent to one another.` `All examples in this Problem feature four of these triangles connected by corners and/or edges.`
	CROSSREFS	`BP897 was conceived as a false solution for this.` `Adjacent-numbered pages: BP893 BP894 BP895 BP896 BP897 * BP899 BP900 BP901 BP902 BP903`
	KEYWORD	`hard, precise, allsorted, notso, math, preciseworld`
	CONCEPT	`triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Molly C Klenzak`

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