The On-Line Encyclopedia of Bongard Problems

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The tightest-curved section, out of all sections of curve that make a complete turn (360 degrees), contains an x-crossing point vs. not so.

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	COMMENTS	`All examples are connected smooth curves allowed to self-intersect that must curve in only one direction (starting at one end, either clockwise or counter-clockwise), i.e. there is no inflection point.`
	CROSSREFS	`Adjacent-numbered pages: BP208 BP209 BP210 BP211 BP212 * BP214 BP215 BP216 BP217 BP218`
	KEYWORD	`less, convoluted, perfect, traditional`
	CONCEPT	`x-crossing (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP227

Dots touch each other if and only if no large region touches the edges of the box vs. dots dont touch each other if and only if no large region touches the edges of the box.

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	CROSSREFS	`Adjacent-numbered pages: BP222 BP223 BP224 BP225 BP226 * BP228 BP229 BP230 BP231 BP232`
	KEYWORD	`convoluted, traditional`
	CONCEPT	`iff (info \| search),` `near_far (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP228

After rotating so that the longest line is horizontal, there is a left arm raised and a weight down vs. after rotating so that the longest line is horizontal, there is a left arm down and a weight raised.

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	CROSSREFS	`Adjacent-numbered pages: BP223 BP224 BP225 BP226 BP227 * BP229 BP230 BP231 BP232 BP233`
	KEYWORD	`convoluted, traditional`
	CONCEPT	`rotation_required (info \| search),` `specific_style (info \| search),` `specificity (info \| search)`
	AUTHOR	`Giuseppe Insana`

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`

BP262

Exactly one point where lines bend at an angle vs. not exactly one point where lines bend at an angle.

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	CROSSREFS	`Adjacent-numbered pages: BP257 BP258 BP259 BP260 BP261 * BP263 BP264 BP265 BP266 BP267`
	KEYWORD	`less, convoluted, traditional`
	CONCEPT	`angle (info \| search),` `number (info \| search)`
	AUTHOR	`Pablo Barenbaum`

BP290

If any non-nosed faces exist, they are happy if and only if happy nosed faces exist as well vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP285 BP286 BP287 BP288 BP289 * BP291 BP292 BP293 BP294 BP295`
	KEYWORD	`convoluted`
	CONCEPT	`existence (info \| search),` `iff (info \| search)`
	AUTHOR	`"Lewis"`

BP825

Ticks mark an infinite sequence of angles on circle such that each angle is the double of the subsequent angle in the sequence (angle measured from rightmost indicated point) vs. not so.

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	COMMENTS	`This is solvable; it was solved by Sridhar Ramesh.` `A full turn is considered "the same angle" as no turns; likewise for adding and subtracting full turns from any angle. All sequences of angles shown start at the rightmost tick.` `It doesn't matter whether the angle is measured clockwise or counterclockwise, as long as the choice is consistent.`
	CROSSREFS	`Adjacent-numbered pages: BP820 BP821 BP822 BP823 BP824 * BP826 BP827 BP828 BP829 BP830`
	KEYWORD	`hard, convoluted, notso, math, solved`
	CONCEPT	`sequence (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP849

Loop is time-symmetrical (loop is like ABCBABCBA... instead of like ABCABCABC...) up to rotation of object vs. not so (neither up to rotation nor reflection).

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	CROSSREFS	`Adjacent-numbered pages: BP844 BP845 BP846 BP847 BP848 * BP850 BP851 BP852 BP853 BP854`
	KEYWORD	`hard, convoluted, solved, rules`
	WORLD	`constant_change_seq_loop_right [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP920

Is exact specific image (EX6205) vs. is not.

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	COMMENTS	`A spot-the-difference exercise.` `Arguably invalid (solution not simple).`
	CROSSREFS	`Adjacent-numbered pages: BP915 BP916 BP917 BP918 BP919 * BP921 BP922 BP923 BP924 BP925`
	KEYWORD	`less, precise, convoluted, arbitrary, stretch, unstable, left-finite, left-full, perfect, pixelperfect, experimental, funny`
	CONCEPT	`imperfection_small (info \| search),` `specificity (info \| search)`
	WORLD	`bmp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP973

Transitive vs. non-transitive relations between the red and blue circles.

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	COMMENTS	Each example in this Bongard Problem consists of mini-panels containing the same arrangement of circles (ignoring colouring). Each mini-panel has a single circle highlighted in red, and possibly some circles highlighted in blue. A strict rule for this Bongard Problem could be something like "If a circle is blue in one mini-panel and red in a second mini-panel, then there are no blue circles in the second mini-panel that weren't already blue in the first mini-panel." The relation interpretation is that a circle is related to the red circle if and only if it is coloured blue.
	CROSSREFS	`Adjacent-numbered pages: BP968 BP969 BP970 BP971 BP972 * BP974 BP975 BP976 BP977 BP978`
	KEYWORD	`convoluted, color, infodense, rules`
	AUTHOR	`Jago Collins`

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