The On-Line Encyclopedia of Bongard Problems

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Opposite (inverse) transformations have been applied to the same specific small square on opposite sides of the dividing line versus not so.

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	COMMENTS	`The original pre-transformed square is the same across all examples, however it is not shown in most examples; what the pre-transformed square looks like must be deduced by the solver.`
	CROSSREFS	`BP1260 is about applying the same transformation to different objects.` `Adjacent-numbered pages: BP834 BP835 BP836 BP837 BP838 * BP840 BP841 BP842 BP843 BP844`
	KEYWORD	`easy, abstract, arbitrary, anticomputer, traditional, rules`
	CONCEPT	`square (info \| search),` `specificity (info \| search),` `function (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Triangle points to center of circle vs. triangle does not point to center of circle.

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	CROSSREFS	`Adjacent-numbered pages: BP112 BP113 BP114 BP115 BP116 * BP118 BP119 BP120 BP121 BP122`
	KEYWORD	`traditional`
	CONCEPT	`between (info \| search),` `on_line_or_curve (info \| search),` `midpoint (info \| search),` `pointing_to (info \| search),` `center_of_circle (info \| search),` `center (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `triangle_arrow (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Long distance between the marked locations vs. short distance between the marked locations.

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	CROSSREFS	`Adjacent-numbered pages: BP309 BP310 BP311 BP312 BP313 * BP315 BP316 BP317 BP318 BP319`
	KEYWORD	`traditional`
	CONCEPT	`length_line_or_curve (info \| search),` `maze (info \| search),` `path (info \| search)`
	AUTHOR	`Jakub Štepo`

Image of a Bongard Problem with no simple solution versus image of a Bongard Problem with a simple solution.

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	COMMENTS	`Left examples have no solution, but they do not break the rules in ways so extreme that it is plainly impossible for them to have a solution, such as including the same image on both sides or including no images per side. (See such as including the same image on both sides or including no images per side.`
	CROSSREFS	`See BP522 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).` `See BP968 (flipped) for a version of this Bongard Problem including examples of invalid Bongard Problems that don't even admit a convoluted solution (the same image appears on both sides).` `Also see BP1080, which is similar to BP968, but including various different formats of Bongard Problems, distinguishing them from arbitrary images that are not Bongard Problems.` `Adjacent-numbered pages: BP824 BP825 BP826 BP827 BP828 * BP830 BP831 BP832 BP833 BP834`
	KEYWORD	`nice, meta (see left/right), miniproblems, creativeexamples, left-unknowable, right-narrow, assumesfamiliarity, structure, help, presentationinvariant`
	CONCEPT	`existence (info \| search),` `simplicity (info \| search),` `zero (info \| search)`
	WORLD	`boxes_bpimage_three_per_side_nosoln_allowed [smaller \| same \| bigger] zoom in right (boxes_bpimage_three_per_side)`
	AUTHOR	`Aaron David Fairbanks`

Net corresponds to a solid that can tessellate 3D space vs. net does not correspond to a solid that can tessellate 3D space.

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	COMMENTS	`More specifically these solids are polyhedra, and are often called "space-filling".` `There is ambiguity here regarding some nets that can be folded to make multiple different solids. For example EX8175 could correspond to a cuboid with a pyramid-like protrusion at each end, a protrusion at one end and an indent at the other, or 2 indents. Only the second of these options can tessellate 3D space. For clarity's sake examples like this are not sorted on either side.`
	CROSSREFS	`Adjacent-numbered pages: BP989 BP990 BP991 BP992 BP993 * BP995 BP996 BP997 BP998 BP999`
	KEYWORD	`stub, precise, 3d, perfect, preciseworld`
	CONCEPT	`3d_net (info \| search),` `3d_solid (info \| search)`
	WORLD	`polyhedron_net [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

Three collinear and two others, the two are vertical vs. the two are horizontal.

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	CROSSREFS	`Adjacent-numbered pages: BP142 BP143 BP144 BP145 BP146 * BP148 BP149 BP150 BP151 BP152`
	KEYWORD	`traditional`
	CONCEPT	`collinear (info \| search),` `horizontal (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `vertical (info \| search),` `two (info \| search),` `three (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Box divided into six areas vs. box divided into four areas.

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	CROSSREFS	`Adjacent-numbered pages: BP227 BP228 BP229 BP230 BP231 * BP233 BP234 BP235 BP236 BP237`
	KEYWORD	`arbitrary, number, traditional`
	CONCEPT	`number (info \| search)`
	AUTHOR	`Giuseppe Insana`

Same transformation applied to circle, triangle, and square vs. different transformations applied.

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	CROSSREFS	`BP839 is about applying opposite transformations to a single object.` `Adjacent-numbered pages: BP1255 BP1256 BP1257 BP1258 BP1259 * BP1261 BP1262 BP1263 BP1264 BP1265`
	KEYWORD	`easy, nice, abstract, arbitrary, anticomputer, left-null, structure, orderedtriplet, traditional, rules`
	CONCEPT	`circle (info \| search),` `analogy (info \| search),` `square (info \| search),` `same (info \| search),` `triangle (info \| search),` `function (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Contains self somewhere within any area around any point within self vs. not so.

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	COMMENTS	`Very similar to the less clearly-defined solution "tiles itself with infinitely many copies (different sizes allowed) vs. does not".` `The left hand side of this is a weaker condition than the left hand side of BP1241.`
	CROSSREFS	`Adjacent-numbered pages: BP1111 BP1112 BP1113 BP1114 BP1115 * BP1117 BP1118 BP1119 BP1120 BP1121`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`topological_density (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`connected_fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Vertical axis of symmetry vs. no vertical axis of symmetry.

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	COMMENTS	`The solution for this Bongard Problem is also a (less specific) solution for BP500, "vertical axis of symmetry vs. no axis of symmetry".`
	CROSSREFS	`BP1207 is the same solution but using the horizontal axis instead of the vertical axis.` `BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.` `Adjacent-numbered pages: BP1201 BP1202 BP1203 BP1204 BP1205 * BP1207 BP1208 BP1209 BP1210 BP1211`
	KEYWORD	`stub, notso, stretch, left-narrow, traditional`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search),` `vertical (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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