The On-Line Encyclopedia of Bongard Problems

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Unconnected circles on a horizontal line vs. unconnected circles on a vertical line.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 235.`
	CROSSREFS	`Adjacent-numbered pages: BP61 BP62 BP63 BP64 BP65 * BP67 BP68 BP69 BP70 BP71`
	KEYWORD	`noisy, finished, traditional, bongard`
	CONCEPT	`collinear (info \| search),` `horizontal (info \| search),` `on_line_or_curve (info \| search),` `shape_cluster (info \| search),` `cluster (info \| search),` `vertical (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

The long axes of the ellipse and rectangle are perpendicular vs. the long axes of the ellipse and rectangle are parallel.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 238.`
	CROSSREFS	`Adjacent-numbered pages: BP68 BP69 BP70 BP71 BP72 * BP74 BP75 BP76 BP77 BP78`
	KEYWORD	`noisy, finished, traditional, bongard`
	CONCEPT	`imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `parallel (info \| search),` `perpendicular (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

The convex hull of the crosses forms an equilateral triangle vs. the convex hull of the crosses does not form an equilateral triangle.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 241.`
	CROSSREFS	`Adjacent-numbered pages: BP77 BP78 BP79 BP80 BP81 * BP83 BP84 BP85 BP86 BP87`
	KEYWORD	`noisy, notso, finished, traditional, bongard`
	CONCEPT	`convex_hull (info \| search),` `equilateral_triangle (info \| search),` `triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

Triangles vs. quadrangles.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 246.`
	CROSSREFS	`Adjacent-numbered pages: BP93 BP94 BP95 BP96 BP97 * BP99 BP100 BP101 BP102 BP103`
	KEYWORD	`easy, nice, noisy, number, finished, traditional, bongard`
	CONCEPT	`number (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Ends of line point to the same direction vs. ends of line do not point to the same direction.

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	CROSSREFS	`Adjacent-numbered pages: BP100 BP101 BP102 BP103 BP104 * BP106 BP107 BP108 BP109 BP110`
	KEYWORD	`noisy, traditional`
	CONCEPT	`slope_at_endpoint (info \| search),` `tracing_line_or_curve (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Negative slope vs. positive slope.

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	COMMENTS	`All examples feature a white circle and a black circle. The answer refers to the slope of the line connecting the two circles.` `The coloring of the circles is irrelevant.`
	CROSSREFS	`Adjacent-numbered pages: BP101 BP102 BP103 BP104 BP105 * BP107 BP108 BP109 BP110 BP111`
	KEYWORD	`nice, noisy, dual, handed, rotate, orderedpair, traditional`
	CONCEPT	`positive_negative_slope (info \| search),` `line_slope (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Circle on the right of the box vs. circle on the left of the box.

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	CROSSREFS	`Adjacent-numbered pages: BP104 BP105 BP106 BP107 BP108 * BP110 BP111 BP112 BP113 BP114`
	KEYWORD	`noisy, dual, handed, leftright, traditional`
	CONCEPT	`absolute_position (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Polygon stands on side vs. polygon stands on vertex.

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	CROSSREFS	`Adjacent-numbered pages: BP111 BP112 BP113 BP114 BP115 * BP117 BP118 BP119 BP120 BP121`
	KEYWORD	`noisy, traditional`
	CONCEPT	`base (info \| search),` `horizontal (info \| search),` `uppermost_lowermost (info \| search),` `vertex_of_meeting_lines (info \| search),` `vertical (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Similar shapes vs. dissimilar shapes.

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	CROSSREFS	`Adjacent-numbered pages: BP118 BP119 BP120 BP121 BP122 * BP124 BP125 BP126 BP127 BP128`
	KEYWORD	`noisy, traditional`
	CONCEPT	`similar_shape (info \| search),` `similar (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Exactly one circle vs. not exactly one circle.

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	CROSSREFS	`Adjacent-numbered pages: BP122 BP123 BP124 BP125 BP126 * BP128 BP129 BP130 BP131 BP132`
	KEYWORD	`noisy, notso, traditional`
	CONCEPT	`exists_one (info \| search),` `number (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

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