The On-Line Encyclopedia of Bongard Problems

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

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

	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`

Lines plus triangles equal stars vs. lines minus triangles equal stars.

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	CROSSREFS	`Adjacent-numbered pages: BP228 BP229 BP230 BP231 BP232 * BP234 BP235 BP236 BP237 BP238`
	KEYWORD	`traditional`
	CONCEPT	`addition (info \| search),` `number (info \| search)`
	AUTHOR	`Peter Shanahan`

Bottom object in front of top objects in 3-D vs. bottom object behind top objects in 3-D.

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

	CROSSREFS	`Adjacent-numbered pages: BP190 BP191 BP192 BP193 BP194 * BP196 BP197 BP198 BP199 BP200`
	KEYWORD	`experimental, dithering`
	CONCEPT	`3d_front_back (info \| search),` `3d_depth (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Harry E. Foundalis`

Can fold into tetragonal disphenoid ("isosceles tetrahedron") vs. cannot.

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	COMMENTS	`Which two sides are the long sides and which side is the short side, or equivalently which angles are the wider angles and which angle is the narrower angle, is the only relevant information to consider for each triangle. Triangles are all assumed isosceles and congruent to one another.` `All examples in this Problem feature four of these triangles connected by corners and/or edges.`
	CROSSREFS	`BP897 was conceived as a false solution for this.` `Adjacent-numbered pages: BP893 BP894 BP895 BP896 BP897 * BP899 BP900 BP901 BP902 BP903`
	KEYWORD	`hard, precise, allsorted, notso, math, preciseworld`
	CONCEPT	`triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Molly C Klenzak`

Filled completely by fluid poured into gap (assuming there is already air) vs. not so.

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	COMMENTS	`For a non-physics-based solution, "there exists a never-vertically-increasing path starting from the opening to each point in the interior vs. not so." - Aaron David Fairbanks, Aug 01 2020`
	CROSSREFS	`Adjacent-numbered pages: BP891 BP892 BP893 BP894 BP895 * BP897 BP898 BP899 BP900 BP901`
	KEYWORD	`nice, handed, updown, physics`
	CONCEPT	`liquid_flow (info \| search),` `gravity (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Zane Fry`

Equal numbers of straight lines and continuous curves vs. unequal numbers of straight lines and continuous curves.

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

	CROSSREFS	`Adjacent-numbered pages: BP241 BP242 BP243 BP244 BP245 * BP247 BP248 BP249 BP250 BP251`
	KEYWORD	`traditional`
	CONCEPT	`curved_straight (info \| search),` `number (info \| search)`
	AUTHOR	`Carla Rispoli`

Shapes identical after rotation vs. shapes identical after rotation and mirroring.

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

	CROSSREFS	`Adjacent-numbered pages: BP300 BP301 BP302 BP303 BP304 * BP306 BP307 BP308 BP309 BP310`
	KEYWORD	`nice, unorderedpair, traditional`
	CONCEPT	`rotation_required (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`"Lewis"`

Any one gear turns all vs. no gear turns all.

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	CROSSREFS	`See BP536 for all gears can turn.` `Adjacent-numbered pages: BP331 BP332 BP333 BP334 BP335 * BP337 BP338 BP339 BP340 BP341`
	KEYWORD	`nice, stretch, physics, traditional`
	CONCEPT	`all (info \| search),` `turn_orientation (info \| search),` `every_other (info \| search),` `gear (info \| search),` `on_line_or_curve (info \| search),` `tracing_line_or_curve (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	WORLD	`gears [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

Nesting vs. no nesting.

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	CROSSREFS	`See BP1061 for a version of this with only squares and which allows infinite nesting.` `See BP71 for a Problem about counting levels of nesting.` `Adjacent-numbered pages: BP1017 BP1018 BP1019 BP1020 BP1021 * BP1023 BP1024 BP1025 BP1026 BP1027`
	KEYWORD	`easy, nice, precise, allsorted, traditional`
	CONCEPT	`recursion_number (info \| search),` `separated_regions (info \| search),` `inside (info \| search),` `recursion (info \| search)`
	WORLD	`varied_thickness_curves_drawing [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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