The On-Line Encyclopedia of Bongard Problems

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Can be cut into tiles forming a checkerboard pattern vs. not so.

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	COMMENTS	`All examples in this Problem are grids consisting of two objects.`
	CROSSREFS	`Adjacent-numbered pages: BP1118 BP1119 BP1120 BP1121 BP1122 * BP1124 BP1125 BP1126 BP1127 BP1128`
	EXAMPLE	`EX9124 shows a 9 square by 9 square grid. Take each tile to be 3 squares by 3 squares; there is a 3 tile by 3 tile checkerboard pattern. (One of these tiles is itself a checkerboard pattern; the other is all black squares.)`
	KEYWORD	`hard, nice, precise, allsorted, hardsort, grid, miniworlds`
	CONCEPT	`element_grouping (info \| search)`
	AUTHOR	`Jago Collins`

Odd number of squares vs. even number of squares.

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	CROSSREFS	`Adjacent-numbered pages: BP145 BP146 BP147 BP148 BP149 * BP151 BP152 BP153 BP154 BP155`
	KEYWORD	`number, traditional`
	CONCEPT	`even_odd (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Gluing sides with the same symbols makes a sphere vs. gluing sides with the same symbols makes a torus.

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	CROSSREFS	`Adjacent-numbered pages: BP365 BP366 BP367 BP368 BP369 * BP371 BP372 BP373 BP374 BP375`
	KEYWORD	`math`
	CONCEPT	`topological_transformation (info \| search),` `3d_solid (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

T-like junction vs. y-like junction.

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	CROSSREFS	`Adjacent-numbered pages: BP108 BP109 BP110 BP111 BP112 * BP114 BP115 BP116 BP117 BP118`
	KEYWORD	`traditional`
	CONCEPT	`branch_point (info \| search),` `t-point (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

One area unreachable by the marked locations vs. all areas reachable by the marked locations.

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	CROSSREFS	`Adjacent-numbered pages: BP310 BP311 BP312 BP313 BP314 * BP316 BP317 BP318 BP319 BP320`
	KEYWORD	`traditional`
	CONCEPT	`maze (info \| search),` `reachable (info \| search)`
	AUTHOR	`Jakub Štepo`

Infinitely many branches vs. finitely many branches.

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	CROSSREFS	`Adjacent-numbered pages: BP1064 BP1065 BP1066 BP1067 BP1068 * BP1070 BP1071 BP1072 BP1073 BP1074`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`finite_infinite (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Two clearly separable groups vs. not so.

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	COMMENTS	`An image of this Bongard Problem will fit as a left example for itself.`
	CROSSREFS	`Adjacent-numbered pages: BP359 BP360 BP361 BP362 BP363 * BP365 BP366 BP367 BP368 BP369`
	KEYWORD	`nice, fuzzy, right-null, contributepairs, traditional, miniworlds`
	CONCEPT	`feature_cluster (info \| search),` `cluster (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Triangles vs. quadrangles.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 245.`
	CROSSREFS	`Adjacent-numbered pages: BP91 BP92 BP93 BP94 BP95 * BP97 BP98 BP99 BP100 BP101`
	KEYWORD	`number, finished, traditional, bongard`
	CONCEPT	`collinear (info \| search),` `line_or_curve_endpoint (info \| search),` `number (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Three parts vs. four parts.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 243.`
	CROSSREFS	`Adjacent-numbered pages: BP85 BP86 BP87 BP88 BP89 * BP91 BP92 BP93 BP94 BP95`
	KEYWORD	`number, finished, traditional, bongard`
	CONCEPT	`number (info \| search),` `outlined_filled (info \| search),` `separation_of_joined_objects (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `texture (info \| search),` `three (info \| search),` `four (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

The end of the right branch is higher than that of the left branch vs. the end of the right branch is lower than that of the left branch.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 236.`
	CROSSREFS	`Adjacent-numbered pages: BP63 BP64 BP65 BP66 BP67 * BP69 BP70 BP71 BP72 BP73`
	KEYWORD	`finished, traditional, viceversa, bongard`
	CONCEPT	`above_below (info \| search),` `branch_point (info \| search),` `line_or_curve_endpoint (info \| search),` `left_right (info \| search),` `tracing_line_or_curve (info \| search)`
	WORLD	`curve_tree_one_branch_per_side [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

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