The On-Line Encyclopedia of Bongard Problems

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Grid of analogies vs. different kind of rule.

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	COMMENTS	`On the left, each row and column could be labeled by a certain object or concept; on the right this is not so.` `More specifically: on the left, each row and each column is associated with a certain object or concept; there is a rule for combining rows and columns to give images; it would be possible without changing the rule to extend with new rows/columns or delete/reorder any existing columns. On the right, this is not so; the rule might be about how the images must relate to their neighbors, for example.` `All examples show grids of squares with an image in each square, such that there is some "rule" the images within the grid obey.` `Left examples are a generalized version of the analogy grids seen in BP361. Any analogy a : b :: c : d shown in a 2x2 grid will fit on the left here.` `To word the solution with mathematical jargon, "defines a (simply described) map from the Cartesian product of two sets vs. not so." Another equivalent solution is "columns (alternatively, rows) illustrate a consistent set of one-input operations." It is always possible to imagine the columns as inputs and the rows as operations and vice versa.` `There is a trivial way in which any example can be interpreted so that it fits on the left side: imagine each row is assigned the list of all the squares in that row and each column is assigned its number, counting from the left. But each grid has a clear rule that is simpler than this.`
	CROSSREFS	`BP1258 is a similar idea: "any square removed could be reconstructed vs. not." Examples included left here usually fit left there, but some do not e.g. EX9998.` `See BP979 for use of similar structures but with one square removed from the grid.` `Adjacent-numbered pages: BP976 BP977 BP978 BP979 BP980 * BP982 BP983 BP984 BP985 BP986`
	KEYWORD	`nice, convoluted, unwordable, notso, teach, structure, rules, grid, miniworlds`
	CONCEPT	`analogy (info \| search)`
	WORLD	`grid_of_images_with_rule [smaller \| same \| bigger] zoom in left (grid_of_analogies)`
	AUTHOR	`Aaron David Fairbanks`

BP987

Solution could appear in a Bongard Problem featuring an image of itself on either of its sides vs. solution can appear in a Bongard Problem featuring an image of itself on a certain side only.

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	COMMENTS	`All examples are Bongard Problems fitting left in BP954.` `This is very close to BP927, specialized to Bongard Problems fitting left in BP954. The difference is that a Bongard Problem solution would fit left in BP927 but right here if it can sort images of it on both sides, but it is impossible to make an image of it fractally including itself on a certain side. An example is EX7997.` `Meta Bongard Problems appearing in BP793 that are presentationinvariant necessarily fit right here.`
	CROSSREFS	`Adjacent-numbered pages: BP982 BP983 BP984 BP985 BP986 * BP988 BP989 BP990 BP991 BP992`
	KEYWORD	`abstract, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant, visualimagination`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1024

One sorted left vs. one sorted right.

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	CROSSREFS	`Adjacent-numbered pages: BP1019 BP1020 BP1021 BP1022 BP1023 * BP1025 BP1026 BP1027 BP1028 BP1029`
	KEYWORD	`precise, allsorted, dual, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1025

Two consecutive numbers sorted left vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1020 BP1021 BP1022 BP1023 BP1024 * BP1026 BP1027 BP1028 BP1029 BP1030`
	KEYWORD	`precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1026

Not an inequality solution vs. inequality solution.

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	CROSSREFS	`Adjacent-numbered pages: BP1021 BP1022 BP1023 BP1024 BP1025 * BP1027 BP1028 BP1029 BP1030 BP1031`
	KEYWORD	`precise, allsorted, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1027

Solution is "one dot vs. more than one dot" vs. other solution.

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	CROSSREFS	`Adjacent-numbered pages: BP1022 BP1023 BP1024 BP1025 BP1026 * BP1028 BP1029 BP1030 BP1031 BP1032`
	KEYWORD	`precise, allsorted, notso, arbitrary, handed, leftright, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1028

An even number is the least sorted left vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1023 BP1024 BP1025 BP1026 BP1027 * BP1029 BP1030 BP1031 BP1032 BP1033`
	KEYWORD	`precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1029

Multiple distinct differences between successive left numbers vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1024 BP1025 BP1026 BP1027 BP1028 * BP1030 BP1031 BP1032 BP1033 BP1034`
	KEYWORD	`precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1030

"Specific number vs. other number" vs. other solution.

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	CROSSREFS	`Adjacent-numbered pages: BP1025 BP1026 BP1027 BP1028 BP1029 * BP1031 BP1032 BP1033 BP1034 BP1035`
	KEYWORD	`precise, allsorted, notso, handed, leftright, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1031

"Less than ___ vs. greater than ___" vs. other solution.

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	CROSSREFS	`See the twin BP1039.` `Adjacent-numbered pages: BP1026 BP1027 BP1028 BP1029 BP1030 * BP1032 BP1033 BP1034 BP1035 BP1036`
	KEYWORD	`precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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