The On-Line Encyclopedia of Bongard Problems

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BP32

A sharp projection vs. no sharp projection.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.`
	CROSSREFS	`Adjacent-numbered pages: BP27 BP28 BP29 BP30 BP31 * BP33 BP34 BP35 BP36 BP37`
	KEYWORD	`nice, notso, finished, traditional, bongard`
	CONCEPT	`acute (info \| search),` `angle (info \| search),` `cusp (info \| search),` `protrusion (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP77

Angle divided in half vs. angle not divided in half.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 239.`
	CROSSREFS	`Adjacent-numbered pages: BP72 BP73 BP74 BP75 BP76 * BP78 BP79 BP80 BP81 BP82`
	KEYWORD	`nice, notso, stretch, finished, traditional, bongard`
	CONCEPT	`angle (info \| search),` `half (info \| search),` `same_feature (info \| search),` `same (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP82

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`

BP127

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`

BP243

Triangle closer to box corner than any of the circles vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP238 BP239 BP240 BP241 BP242 * BP244 BP245 BP246 BP247 BP248`
	KEYWORD	`notso, boundingbox, traditional, absoluteposition`
	CONCEPT	`bounding_box_corner (info \| search),` `length_line_or_curve (info \| search),` `near_far (info \| search),` `triangle (info \| search)`
	AUTHOR	`Matthew J. Howells`

BP257

The distance from the center of the line to the bottom of the square is the same as the distance from the dot to the right edge of the square vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP252 BP253 BP254 BP255 BP256 * BP258 BP259 BP260 BP261 BP262`
	KEYWORD	`convoluted, notso, boundingbox, traditional, absoluteposition`
	CONCEPT	`bounding_box (info \| search),` `length_line_or_curve (info \| search),` `midpoint (info \| search),` `imagined_point (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `same_feature (info \| search),` `same (info \| search),` `distance_from_center (info \| search)`
	AUTHOR	`Andreas Gunnarsson`

BP274

Notch from above (holds poured water) vs. no notch from above (does not hold poured water).

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	CROSSREFS	`Adjacent-numbered pages: BP269 BP270 BP271 BP272 BP273 * BP275 BP276 BP277 BP278 BP279`
	KEYWORD	`notso, physics`
	CONCEPT	`concave_convex_region (info \| search),` `downward_upward (info \| search),` `line_absolute_direction (info \| search),` `absolute_direction (info \| search),` `direction (info \| search),` `liquid_flow (info \| search),` `gravity (info \| search)`
	WORLD	`arial_font_centered_connected_symbol [smaller \| same \| bigger]`
	AUTHOR	`Merse E. Gáspár`

BP288

The sum of the ratios of the filled areas is 1 vs. the sum of the ratios of the filled areas is other than 1.

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	CROSSREFS	`Adjacent-numbered pages: BP283 BP284 BP285 BP286 BP287 * BP289 BP290 BP291 BP292 BP293`
	KEYWORD	`nice, notso, traditional`
	CONCEPT	`addition (info \| search),` `outlined_filled (info \| search),` `ratio (info \| search),` `texture (info \| search)`
	AUTHOR	`"Lewis"`

BP323

Jigsaw puzzle pieces can be assembled into a square vs. jigsaw puzzle pieces cannot be assembled into a square.

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	COMMENTS	`Although it takes time to check each individual example, the right answer is likely the first thing a person would think of upon seeing this.`
	CROSSREFS	`Adjacent-numbered pages: BP318 BP319 BP320 BP321 BP322 * BP324 BP325 BP326 BP327 BP328`
	KEYWORD	`notso, hardsort`
	CONCEPT	`jigsaw_puzzle (info \| search),` `tiling (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP344

Shape can tile itself vs. shape cannot tile itself.

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	COMMENTS	`Left examples are sometimes called "rep-tiles."` `The tiles all must be the same size. More specifically, all left examples can tile themselves only using scaled down and rotated versions of themselves with all tiles the same size. Right examples cannot tile themselves using scaled down rotated versions of themselves or even reflected versions of themselves with all tiles the same size.` `Without the puzzle piece-like shape EX4120 on the right side the current examples also allow the solution "shape can tile with itself so as to create a parallelogram vs. shape cannot tile with itself so as to create a parallelogram."`
	CROSSREFS	`See BP532 for a version with fractals.` `Adjacent-numbered pages: BP339 BP340 BP341 BP342 BP343 * BP345 BP346 BP347 BP348 BP349`
	EXAMPLE	`Go to https://oebp.org/files/yet.png for an illustration of how some left-sorted shapes tile themselves.`
	KEYWORD	`hard, precise, notso, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, traditional`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`shape [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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