The On-Line Encyclopedia of Bongard Problems

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Process described leaves some inputs invariant vs. no output will resemble its input.

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	COMMENTS	`There are many ambiguities here. The solver is expected to determine what things are "allowed" to be inputs for each process. To avoid confusion examples should not be sorted differently if you consider inputting nothing.` `In each example there is at least some overlap between the set of possible inputs and the set of possible outputs for each process. If we did not apply this constraint, an easy example to be sorted right would be a process that turns blue shapes red.` `A harder-to-read but more clearly defined version of this Problem could include within each example a mini Bongard Problem sorting left all allowed inputs for the process.`
	REFERENCE	`https://en.wikipedia.org/wiki/Fixed_point_(mathematics)`
	CROSSREFS	`Adjacent-numbered pages: BP946 BP947 BP948 BP949 BP950 * BP952 BP953 BP954 BP955 BP956`
	KEYWORD	`structure, rules, miniworlds`
	CONCEPT	`function (info \| search)`
	AUTHOR	`Leo Crabbe`

"No panels vs. dots" or "dots vs. no panels" vs. other dots Bongard Problem.

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	CROSSREFS	`Adjacent-numbered pages: BP1037 BP1038 BP1039 BP1040 BP1041 * BP1043 BP1044 BP1045 BP1046 BP1047`
	KEYWORD	`less, precise, allsorted, notso, meta (see left/right), miniproblems, example, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	CONCEPT	`or (info \| search)`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

A line separates the crosses in half vs. a line does not separate the crosses in half.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 234.`
	CROSSREFS	`Adjacent-numbered pages: BP56 BP57 BP58 BP59 BP60 * BP62 BP63 BP64 BP65 BP66`
	KEYWORD	`finished, traditional, bongard`
	CONCEPT	`sides_of_line (info \| search),` `shape_cluster (info \| search),` `cluster (info \| search),` `same_number (info \| search),` `same (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Stays put vs. tumbles.

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	CROSSREFS	`BP273 has the same solution, except all examples are letters.` `Adjacent-numbered pages: BP194 BP195 BP196 BP197 BP198 * BP200 BP201 BP202 BP203 BP204`
	KEYWORD	`nice, handed, updown, rotate, physics, anticomputer, perfect`
	CONCEPT	`base (info \| search),` `downward_upward (info \| search),` `tumbles_or_stays_put (info \| search),` `line_absolute_direction (info \| search),` `absolute_direction (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `direction (info \| search),` `gravity (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Line divides interior into two regions vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP117 BP118 BP119 BP120 BP121 * BP123 BP124 BP125 BP126 BP127`
	KEYWORD	`traditional`
	CONCEPT	`separated_regions (info \| search),` `interior_exterior (info \| search),` `number (info \| search),` `tiling (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Both players playing "capture game" optimally vs. one or both players make mistakes.

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	COMMENTS	`In the depicted "capture game", the objective is to capture your opponent's piece by moving to a node they are occupying. Players take turns moving their pieces. You can only move to a node that is linked to yours. Optimal play can either lead to a win-lose state or a draw state.` `A frame where only one black disc is visible signifies that a player has taken the other's piece, winning the game.`
	CROSSREFS	`Adjacent-numbered pages: BP1279 BP1280 BP1281 BP1282 BP1283 * BP1285 BP1286 BP1287 BP1288 BP1289`
	KEYWORD	`teach, animated`
	CONCEPT	`capture_game (info \| search)`
	AUTHOR	`Leo Crabbe`

Odd number of enclosed regions vs. even number of enclosed regions.

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	COMMENTS	`The use of numbers and pictures are only a distraction.` `See BP966 for the version in which the background counts.`
	CROSSREFS	`Adjacent-numbered pages: BP884 BP885 BP886 BP887 BP888 * BP890 BP891 BP892 BP893 BP894`
	KEYWORD	`number`
	CONCEPT	`separated_regions (info \| search),` `even_odd (info \| search)`
	AUTHOR	`Thomas Joyce`

Graph can be redrawn such that no edges intersect vs. not so.

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	COMMENTS	`A graph is a collection of vertices and edges. Vertices are the dots and edges are the lines that connect the dots. On the left, all edges can be redrawn (curved lines are allowed and moving vertices is allowed) such that no edges cross each other and each vertex is still connected to the same other vertices. These graphs are called planar.`
	CROSSREFS	`Adjacent-numbered pages: BP900 BP901 BP902 BP903 BP904 * BP906 BP907 BP908 BP909 BP910`
	KEYWORD	`nice, precise, allsorted, notso, math, left-null, preciseworld`
	CONCEPT	`graph (info \| search),` `topological_transformation (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Molly C Klenzak`

Bongard Problem with solution based on features vs. Bongard Problem with solution based on number.

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	COMMENTS	`Every example is an image of a Bongard Problem, without bounding boxes around examples, with three examples on either side.`
	CROSSREFS	`BP575 is similar.` `Adjacent-numbered pages: BP195 BP196 BP197 BP198 BP199 * BP201 BP202 BP203 BP204 BP205`
	KEYWORD	`nice, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, experimental, presentationinvariant`
	CONCEPT	`bongard_problem (info \| search),` `bp_solution (info \| search)`
	WORLD	`no_box_bpimage_three_drawings_per_side [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

Two circles close to each other vs. no two circles close to each other.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.`
	CROSSREFS	`Adjacent-numbered pages: BP46 BP47 BP48 BP49 BP50 * BP52 BP53 BP54 BP55 BP56`
	KEYWORD	`nice, finished, traditional, bongard`
	CONCEPT	`near_far (info \| search)`
	WORLD	`four_dot_outlines [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

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