The On-Line Encyclopedia of Bongard Problems

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Prime knot vs. composite knot.

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	REFERENCE	`https://en.wikipedia.org/wiki/Prime_knot`
	CROSSREFS	`Adjacent-numbered pages: BP848 BP849 BP850 BP851 BP852 * BP854 BP855 BP856 BP857 BP858`
	KEYWORD	`math, hardsort`
	CONCEPT	`knot (info \| search)`
	WORLD	`knot [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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`

Regular star polygon vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP335 BP336 BP337 BP338 BP339 * BP341 BP342 BP343 BP344 BP345`
	KEYWORD	`math, traditional`
	CONCEPT	`tracing_line_or_curve (info \| search),` `vertex_of_meeting_lines (info \| search),` `write_in_single_stroke (info \| search)`
	WORLD	`figure_made_of_segments [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Closed curves clockwise, open curves counterclockwise vs. closed curves counterclockwise, open curves clockwise.

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	CROSSREFS	`Adjacent-numbered pages: BP308 BP309 BP310 BP311 BP312 * BP314 BP315 BP316 BP317 BP318`
	KEYWORD	`dual, handed, leftright, updown, traditional`
	CONCEPT	`turn_orientation (info \| search),` `closed_open (info \| search)`
	AUTHOR	`Jakub Štepo`

Three spatially separated clusters vs. two spatially separated clusters.

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	CROSSREFS	`Adjacent-numbered pages: BP151 BP152 BP153 BP154 BP155 * BP157 BP158 BP159 BP160 BP161`
	KEYWORD	`traditional`
	CONCEPT	`number (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `two (info \| search),` `three (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

All boxes on each particular nesting depth have the same number of boxes in them vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1060 BP1061 BP1062 BP1063 BP1064 * BP1066 BP1067 BP1068 BP1069 BP1070`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Similar textures vs. dissimilar textures.

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	CROSSREFS	`Adjacent-numbered pages: BP119 BP120 BP121 BP122 BP123 * BP125 BP126 BP127 BP128 BP129`
	KEYWORD	`traditional`
	CONCEPT	`same_feature (info \| search),` `same (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Two clusters of three and two vs. two clusters of four and one.

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	CROSSREFS	`Adjacent-numbered pages: BP138 BP139 BP140 BP141 BP142 * BP144 BP145 BP146 BP147 BP148`
	KEYWORD	`traditional`
	CONCEPT	`and (info \| search),` `number (info \| search),` `feature_cluster (info \| search),` `shape_cluster (info \| search),` `cluster (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

Random arrangement of pixels vs. not so.

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	COMMENTS	`By "random" we mean it's reasonable to expect each pixel in the image was chosen with a constant, consistent chance of being black or white.`
	CROSSREFS	`Adjacent-numbered pages: BP354 BP355 BP356 BP357 BP358 * BP360 BP361 BP362 BP363 BP364`
	KEYWORD	`nice, right-narrow, collective, experimental, blackwhiteinvariant`
	CONCEPT	`pattern_or_random (info \| search)`
	WORLD	`bmp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

No dot well within the convex hull vs. at least one dot well within the convex hull.

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	CROSSREFS	`Adjacent-numbered pages: BP133 BP134 BP135 BP136 BP137 * BP139 BP140 BP141 BP142 BP143`
	KEYWORD	`traditional`
	CONCEPT	`convex_hull (info \| search),` `existence (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`5_dots [smaller \| same \| bigger]`
	AUTHOR	`Douglas R. Hofstadter`

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