The On-Line Encyclopedia of Bongard Problems

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Solid dark quadrangles are identical vs. solid dark quadrangles are different.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 233.`
	CROSSREFS	`Adjacent-numbered pages: BP53 BP54 BP55 BP56 BP57 * BP59 BP60 BP61 BP62 BP63`
	KEYWORD	`noisy, finished, traditional, bongard`
	CONCEPT	`identical (info \| search),` `outlined_filled (info \| search),` `square (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `same_shape (info \| search),` `same (info \| search),` `texture (info \| search)`
	AUTHOR	`Mikhail M. Bongard`

Convex hull is a square vs. convex hull is not a square.

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	CROSSREFS	`Adjacent-numbered pages: BP237 BP238 BP239 BP240 BP241 * BP243 BP244 BP245 BP246 BP247`
	KEYWORD	`noisy, traditional`
	CONCEPT	`convex_hull (info \| search),` `square (info \| search)`
	AUTHOR	`Matthew J. Howells`

Shapes, if tiled up properly, form a square vs. shapes cannot form a square no matter how they are tiled.

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	CROSSREFS	`Adjacent-numbered pages: BP284 BP285 BP286 BP287 BP288 * BP290 BP291 BP292 BP293 BP294`
	KEYWORD	`nice, stretch, traditional`
	CONCEPT	`square (info \| search),` `tiling (info \| search)`
	AUTHOR	`"Lewis"`

Square divided into four areas of the same size and shape vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP288 BP289 BP290 BP291 BP292 * BP294 BP295 BP296 BP297 BP298`
	KEYWORD	`nice, traditional`
	CONCEPT	`square (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`"Lewis"`

Opposite (inverse) transformations have been applied to the same specific small square on opposite sides of the dividing line versus not so.

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	COMMENTS	`The original pre-transformed square is the same across all examples, however it is not shown in most examples; what the pre-transformed square looks like must be deduced by the solver.`
	CROSSREFS	`BP1260 is about applying the same transformation to different objects.` `Adjacent-numbered pages: BP834 BP835 BP836 BP837 BP838 * BP840 BP841 BP842 BP843 BP844`
	KEYWORD	`easy, abstract, arbitrary, anticomputer, traditional, rules`
	CONCEPT	`square (info \| search),` `specificity (info \| search),` `function (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Square bounding box vs. oblong rectangular bounding box.

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	CROSSREFS	`Adjacent-numbered pages: BP937 BP938 BP939 BP940 BP941 * BP943 BP944 BP945 BP946 BP947`
	KEYWORD	`precise, stretch, boundingbox, invalid, experimental, preciseworld`
	CONCEPT	`bounding_box (info \| search),` `square (info \| search)`
	WORLD	`rectangular_arrangement_of_white_pixels [smaller \| same \| bigger] zoom in left (square_arrangement_of_white_pixels) \| zoom in right (oblong_rectangular_arrangement_of_white_pixels)`
	AUTHOR	`Leo Crabbe`

Triangle is smallest black shape vs. square is smallest black shape.

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	CROSSREFS	`Adjacent-numbered pages: BP964 BP965 BP966 BP967 BP968 * BP970 BP971 BP972 BP973 BP974`
	KEYWORD	`stub`
	CONCEPT	`size (info \| search),` `square (info \| search),` `triangle (info \| search),` `most (info \| search),` `quantity_comparison (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Polygon that can be achieved by folding a square once vs. other polygons.

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	COMMENTS	`Although it is tempting at first to make a version of this Bongard Problem with the solution "Shape can be achieved by folding a square a finite amount of times vs. other shapes", this alternate Bongard Problem would just amount to having the solution "Convex shape with straight edges vs. concave shape or convex shape with at least one curved edge."`
	CROSSREFS	`Adjacent-numbered pages: BP1140 BP1141 BP1142 BP1143 BP1144 * BP1146 BP1147 BP1148 BP1149 BP1150`
	KEYWORD	`precise, notso, stretch, left-narrow, finishedexamples, preciseworld`
	CONCEPT	`square (info \| search)`
	AUTHOR	`Leo Crabbe`

Empty square present vs. no square present.

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	CROSSREFS	`Nearly identical to BP1221, which is the same except non-empty squares are allowed.` `See BP24 for "circle present vs. not".` `Adjacent-numbered pages: BP1204 BP1205 BP1206 BP1207 BP1208 * BP1210 BP1211 BP1212 BP1213 BP1214`
	KEYWORD	`stub, left-narrow, traditional`
	CONCEPT	`empty (info \| search),` `existence (info \| search),` `square (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Blank image (square) vs. image of blank square.

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	CROSSREFS	`See also BP1056, "blank image vs. nothing".` `BP1 is also a (less specific) solution to this.` `BP1209 (flipped) is also a (less specific) solution to this.` `Adjacent-numbered pages: BP1214 BP1215 BP1216 BP1217 BP1218 * BP1220 BP1221 BP1222 BP1223 BP1224`
	KEYWORD	`minimal, gap, left-narrow, right-narrow, left-finite, right-finite, left-full, right-full, left-null, funny, unstableworld`
	CONCEPT	`empty (info \| search),` `square (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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