The On-Line Encyclopedia of Bongard Problems

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Isosceles triangle vs. scalene triangle.

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	CROSSREFS	`Adjacent-numbered pages: BP98 BP99 BP100 BP101 BP102 * BP104 BP105 BP106 BP107 BP108`
	KEYWORD	`precise, allsorted, stretch, orderedpair, traditional, preciseworld`
	CONCEPT	`line_or_curve_endpoint (info \| search),` `length_line_or_curve (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `same_feature (info \| search),` `same (info \| search),` `isosceles_triangle (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

No axis of symmetry vs. vertical axis of symmetry.

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	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`

Tetrahedron projected on the box plane vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP245 BP246 BP247 BP248 BP249 * BP251 BP252 BP253 BP254 BP255`
	KEYWORD	`stretch, traditional, left-couldbe`
	CONCEPT	`number (info \| search),` `3d_solid (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Andreas Gunnarsson`

Shapes, if tiled up properly, form a square vs. shapes cannot form a square no matter how they are tiled.

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	CROSSREFS	`Adjacent-numbered pages: BP284 BP285 BP286 BP287 BP288 * BP290 BP291 BP292 BP293 BP294`
	KEYWORD	`nice, stretch, traditional`
	CONCEPT	`square (info \| search),` `tiling (info \| search)`
	AUTHOR	`"Lewis"`

All sides are equal vs. all angles are equal.

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	CROSSREFS	`Adjacent-numbered pages: BP323 BP324 BP325 BP326 BP327 * BP329 BP330 BP331 BP332 BP333`
	KEYWORD	`nice, stretch, left-narrow, right-narrow, traditional, finishedexamples, both`
	CONCEPT	`angle (info \| search),` `length_line_or_curve (info \| search),` `same_feature (info \| search),` `same (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Regular polygon vs. not regular polygon.

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	CROSSREFS	`Adjacent-numbered pages: BP324 BP325 BP326 BP327 BP328 * BP330 BP331 BP332 BP333 BP334`
	KEYWORD	`precise, allsorted, stretch, traditional, finishedexamples, preciseworld`
	CONCEPT	`angle (info \| search),` `same_feature (info \| search),` `same (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Drawing of platonic solid (regular polyhedron) vs. drawing of non-platonic solid.

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	CROSSREFS	`Adjacent-numbered pages: BP328 BP329 BP330 BP331 BP332 * BP334 BP335 BP336 BP337 BP338`
	KEYWORD	`stretch, math, 3d, traditional, left-couldbe`
	AUTHOR	`Aaron David Fairbanks`

Tessellates the plane vs. does not tessellate the plane.

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	COMMENTS	`EX7152 is an example of a shape than can be stretched in such a way that it no longer tessellates the plane. This is a property that is only exhibited by shapes that tessellate with rotated copies of themselves. - Leo Crabbe, Mar 05 2021`
	CROSSREFS	`Adjacent-numbered pages: BP330 BP331 BP332 BP333 BP334 * BP336 BP337 BP338 BP339 BP340`
	KEYWORD	`nice, stretch, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, pixelperfect, traditional`
	CONCEPT	`infinite_plane (info \| search),` `tessellation (info \| search),` `tiling (info \| search)`
	WORLD	`shape [smaller \| same \| bigger] zoom in left (fill_shape)`
	AUTHOR	`Aaron David Fairbanks`

Any one gear turns all vs. no gear turns all.

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	CROSSREFS	`See BP536 for all gears can turn.` `Adjacent-numbered pages: BP331 BP332 BP333 BP334 BP335 * BP337 BP338 BP339 BP340 BP341`
	KEYWORD	`nice, stretch, physics, traditional`
	CONCEPT	`all (info \| search),` `turn_orientation (info \| search),` `every_other (info \| search),` `gear (info \| search),` `on_line_or_curve (info \| search),` `tracing_line_or_curve (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	WORLD	`gears [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

Same amount of black in any vertical slice vs. varying amounts of black in vertical slices.

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	CROSSREFS	`Adjacent-numbered pages: BP518 BP519 BP520 BP521 BP522 * BP524 BP525 BP526 BP527 BP528`
	KEYWORD	`nice, precise, rotate, stretch, unstable, perfect, pixelperfect, traditional`
	WORLD	`shapes_can_touch_box [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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