The On-Line Encyclopedia of Bongard Problems

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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`

BP970

Triangle is largest black shape vs. circle is largest black shape.

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	CROSSREFS	`Adjacent-numbered pages: BP965 BP966 BP967 BP968 BP969 * BP971 BP972 BP973 BP974 BP975`
	KEYWORD	`stub`
	CONCEPT	`circle (info \| search),` `size (info \| search),` `triangle (info \| search),` `most (info \| search),` `quantity_comparison (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP971

Left half has more black (less white) than right half versus vice versa.

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	COMMENTS	`A similar, but different, solution is "center of mass is on the left half vs. center of mass is on the right half."`
	CROSSREFS	`See BP972 for the version with examples rotated a quarter-turn.` `Adjacent-numbered pages: BP966 BP967 BP968 BP969 BP970 * BP972 BP973 BP974 BP975 BP976`
	KEYWORD	`nice, precise, spectrum, dual, handed, leftright, rotate, boundingbox, blackwhite, traditional, viceversa, absoluteposition, bordercontent`
	AUTHOR	`Aaron David Fairbanks`

BP972

Top half has more black (less white) than bottom half versus vice versa.

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	COMMENTS	`A similar, but different, solution is "center of mass is above the horizontal vs. center of mass is below the horizontal."`
	CROSSREFS	`See BP971 for the version with examples rotated a quarter-turn.` `Adjacent-numbered pages: BP967 BP968 BP969 BP970 BP971 * BP973 BP974 BP975 BP976 BP977`
	KEYWORD	`precise, spectrum, dual, handed, updown, boundingbox, blackwhite, traditional, viceversa, absoluteposition, bordercontent`
	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`

BP974

"Bounding-box-dependent" Bongard Problems vs. Bongard Problems in which the bounding box can be extended arbitrarily in any direction (in white space) without switching the sorting of any examples.

BP8	BP157	BP209	BP210	BP243	BP257
BP312	BP321	BP525	BP818	BP942	BP966
BP971	BP972	BP1008	BP1014	BP1089	BP1093
BP1104	BP1122	BP1132	BP1156	BP1245

?
BP2

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	COMMENTS	`Left examples have the keyword "boundingbox" on the OEBP.` `Slightly different: sliding the content in a box around without letting it cross the bounding box and without changing the size of the bounding box. (See keyword absoluteposition.)` `Expanding the boxes of BP2 ("big vs. small") makes the contents smaller in comparison to the box, but not smaller in an absolute sense. Hence the situation is ambiguous.`
	CROSSREFS	`If a Bongard Problem has the keyword absoluteposition, then it likely has the keyword boundingbox.` `If a Bongard Problem has the keyword boundingbox and does not have the keyword bordercontent, then it likely has the keyword absoluteposition.` `Adjacent-numbered pages: BP969 BP970 BP971 BP972 BP973 * BP975 BP976 BP977 BP978 BP979`
	KEYWORD	`meta (see left/right), links, keyword, invariance`
	AUTHOR	`Aaron David Fairbanks`

BP975

Symmetric vs. Asymmetric relations between the red and blue circles.

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

	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 the red circle from the first mini-panel is blue in the second mini-panel." The relation intepretation is that a circle is related to the red circle if and only if it is coloured blue. BP973 is a similar problem.
	CROSSREFS	`Adjacent-numbered pages: BP970 BP971 BP972 BP973 BP974 * BP976 BP977 BP978 BP979 BP980`
	KEYWORD	`convoluted, color, infodense, rules`
	AUTHOR	`Jago Collins`

BP976

Bongard Problems that use color in their examples vs. black and white Bongard Problems.

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

	COMMENTS	`Left examples have the keyword "color" on the OEBP.`
	CROSSREFS	`Adjacent-numbered pages: BP971 BP972 BP973 BP974 BP975 * BP977 BP978 BP979 BP980 BP981`
	KEYWORD	`meta (see left/right), links, keyword, wellfounded`
	WORLD	`visualbp [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP977

Two of the same object are enclosed in the same space (there is a path between them) vs. not so.

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	COMMENTS	`An "object" is everything within some black boundary.`
	CROSSREFS	`See BP1071 for a version with only squares and with infinite nesting allowed.` `Adjacent-numbered pages: BP972 BP973 BP974 BP975 BP976 * BP978 BP979 BP980 BP981 BP982`
	KEYWORD	`nice, precise, allsorted, creativeexamples, traditional`
	CONCEPT	`separated_regions (info \| search),` `identical (info \| search),` `recursion (info \| search),` `imagined_line_or_curve (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP978

Bongard Problems in which all examples have a high amount of information that a person must unpack in order to sort them vs. Bongard Problems in which all examples have a low amount of information that a person must unpack in order to sort them.

BP3

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	COMMENTS	`Left examples have the keyword "infodense" on the OEBP.` `Consider the amount of data a person has to consciously unpack in each example in the process of determining how it should be sorted. In BP3, it is only necessary to notice the color of the shape. In BP871, however, it is important to read various qualities of every tiny shape shown.` `Images of Bongard Problems that are "infodense" typically need to include a large number of examples in order to communicate the solution clearly without admitting unintended solutions. With so much data packed in each example, it becomes more likely that some of the random patterns in the data will happen to distinguish between the two sides in an unintended way. A similar issue appears in convoluted Bongard Problems.` `Contrast "infodense" Problems to hardsort Bongard Problems, in which examples are difficult to sort, but perhaps that difficulty does not stem from reading a high amount of information; perhaps there is a small amount of information extracted from the examples, but it is hard to determine whether or not that information fits a rule.`
	CROSSREFS	`Adjacent-numbered pages: BP973 BP974 BP975 BP976 BP977 * BP979 BP980 BP981 BP982 BP983`
	KEYWORD	`abstract, spectrum, meta (see left/right), links, keyword`
	AUTHOR	`Aaron David Fairbanks`

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