The On-Line Encyclopedia of Bongard Problems

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Angle bisectors meet at the incenter vs. perpendicular bisectors meet at the orthocenter.

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	CROSSREFS	`Adjacent-numbered pages: BP166 BP167 BP168 BP169 BP170 * BP172 BP173 BP174 BP175 BP176`
	KEYWORD	`nice, math, traditional`
	CONCEPT	`triangle_incenter (info \| search),` `triangle_orthocenter (info \| search),` `triangle (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Pi-like shape vs. x-like shape.

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	CROSSREFS	`Adjacent-numbered pages: BP165 BP166 BP167 BP168 BP169 * BP171 BP172 BP173 BP174 BP175`
	KEYWORD	`nice, arbitrary, anticomputer, traditional, blackwhiteinvariant`
	CONCEPT	`specific_shape (info \| search),` `specificity (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Two clusters of different numbers of elements vs. two clusters of equal number of elements.

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	CROSSREFS	`Adjacent-numbered pages: BP164 BP165 BP166 BP167 BP168 * BP170 BP171 BP172 BP173 BP174`
	KEYWORD	`traditional`
	CONCEPT	`number (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `same_number (info \| search),` `same (info \| search),` `two (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Bulky interior, if closed vs. narrow interior, if closed.

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	CROSSREFS	`Adjacent-numbered pages: BP163 BP164 BP165 BP166 BP167 * BP169 BP170 BP171 BP172 BP173`
	KEYWORD	`traditional`
	CONCEPT	`elongated_compact (info \| search),` `imperfection_small (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Every cluster has two clusters of dots vs. every cluster has three clusters of dots.

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	CROSSREFS	`Adjacent-numbered pages: BP162 BP163 BP164 BP165 BP166 * BP168 BP169 BP170 BP171 BP172`
	KEYWORD	`traditional`
	CONCEPT	`number (info \| search),` `dot (info \| search),` `recursion (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`Multiple options: dot_clusters [smaller \| same \| bigger], point_clusters [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

Two clusters vs. three clusters.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP161 BP162 BP163 BP164 BP165 * BP167 BP168 BP169 BP170 BP171`
	KEYWORD	`traditional`
	CONCEPT	`number (info \| search),` `dot (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`Multiple options: dot_clusters [smaller \| same \| bigger], point_clusters [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

Line perpendicular to one side of the object vs. line parallel to one side of the object.

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	CROSSREFS	`Adjacent-numbered pages: BP160 BP161 BP162 BP163 BP164 * BP166 BP167 BP168 BP169 BP170`
	KEYWORD	`noisy, orderedpair, traditional`
	CONCEPT	`parallel (info \| search),` `perpendicular (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Number of objects is one less than sides of each object vs. number of objects is one more than sides of each object.

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	CROSSREFS	`Adjacent-numbered pages: BP159 BP160 BP161 BP162 BP163 * BP165 BP166 BP167 BP168 BP169`
	KEYWORD	`nice, traditional`
	CONCEPT	`subtraction (info \| search),` `number (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

Line connecting small shapes does not intersect large one vs. line connecting small shapes intersects large one.

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	CROSSREFS	`See BP1015 for a re-skinned version with dots instead of shapes.` `Adjacent-numbered pages: BP158 BP159 BP160 BP161 BP162 * BP164 BP165 BP166 BP167 BP168`
	KEYWORD	`traditional`
	CONCEPT	`imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `object_line_overlap (info \| search),` `overlap (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Every other side, if extended, passes through one point vs. not so.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP157 BP158 BP159 BP160 BP161 * BP163 BP164 BP165 BP166 BP167`
	KEYWORD	`hard, noisy, traditional`
	CONCEPT	`lines_coincide (info \| search),` `every_other (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search)`
	AUTHOR	`Harry E. Foundalis`

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