The On-Line Encyclopedia of Bongard Problems

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BP833

Image of a Bongard Problem with (left) solution property that can have multiplicity vs. not so.

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	COMMENTS	`All examples are "object present vs. object absent" Problems.`
	CROSSREFS	`Adjacent-numbered pages: BP828 BP829 BP830 BP831 BP832 * BP834 BP835 BP836 BP837 BP838`
	KEYWORD	`abstract, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	CONCEPT	`existence (info \| search),` `number (info \| search),` `one (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP834

Image of a Bongard Problem such that the bottom left box rules out a solution vs. no single box affects the solution.

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	COMMENTS	`When removal of a box changes the solution, it cannot remove the existing solution; it can only allow more possible new solutions. Conversely, adding boxes can only narrow down between existing solutions.` `The special box is always placed in the bottom left for help, but another solution is "there is some box whose removal allows another solution vs. not".` `Bongard Problems sorted left might be called "deceptive". Especially when the solution ruled out by the one box is the more obvious solution.`
	CROSSREFS	`Adjacent-numbered pages: BP829 BP830 BP831 BP832 BP833 * BP835 BP836 BP837 BP838 BP839`
	KEYWORD	`meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure`
	WORLD	`boxes_bpimage_three_per_side [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP835

Image of a Bongard Problem with solution about tiling vs. not so.

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	COMMENTS	`"Tiling" is placing shapes next to each other without overlap to fill up space or other shapes.`
	CROSSREFS	`See BP706 for the version with links to pages on the OEBP instead of images of Bongard Problems.` `Adjacent-numbered pages: BP830 BP831 BP832 BP833 BP834 * BP836 BP837 BP838 BP839 BP840`
	KEYWORD	`meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	CONCEPT	`tiling (info \| search)`
	WORLD	`boxes_bpimage_three_per_side [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP836

Image of a Bongard Problem with solution about a geometrical symmetry (invariance under spatial transformation) vs. not so.

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	COMMENTS	`Every Bongard Problem on the left shows invariance under some transformation in left sub-examples.` `Some Bongard Problems on the right are symmetrical or have sub-examples that are symmetrical.`
	CROSSREFS	`See BP760 for the version with links to pages on the OEBP instead of images of Bongard Problems.` `Adjacent-numbered pages: BP831 BP832 BP833 BP834 BP835 * BP837 BP838 BP839 BP840 BP841`
	KEYWORD	`meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	CONCEPT	`symmetry (info \| search)`
	WORLD	`boxes_bpimage_three_per_side [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP854

Nothing vs. nothing.

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	CROSSREFS	`Adjacent-numbered pages: BP849 BP850 BP851 BP852 BP853 * BP855 BP856 BP857 BP858 BP859`
	KEYWORD	`left-finite, right-finite, left-full, right-full, finished, experimental, funny`
	WORLD	`nothing [same \| bigger] zoom in left (nothing) \| zoom in right (nothing)`
	AUTHOR	`Aaron David Fairbanks`

BP894

Examples fit solution (once it is known) relatively obviously vs. examples fit solution in subtle or complex, harder-to-see ways.

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	COMMENTS	`One left and one right example with each solution are shown for help.` `This BP is fuzzy for multiple reasons. How obvious it is that an example fits a rule is subjective. Also, somebody could read the simplicity of all included examples as part of a Bongard Problem's solution. For example, the more obvious version of "square number of dots vs. non-square number of dots" could be interpreted as "square small number of dots arranged in easy-to-read way vs. non-square small number of dots arranged in easy-to-read way."` `Whether this Bongard Problem solution would categorize an image of itself left or right depends on the difficulty of the solutions of the mini-Problems.`
	CROSSREFS	`See keyword help.` `See keyword hardsort.` `Adjacent-numbered pages: BP889 BP890 BP891 BP892 BP893 * BP895 BP896 BP897 BP898 BP899`
	KEYWORD	`fuzzy, abstract, notso, subjective, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, contributepairs`
	WORLD	`boxes_bpimage_three_per_side [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP927

Image of Bongard Problem whose self-sorting depends on examples in it vs. image of Bongard Problem that will sort any Bongard Problem with its solution on either its left or right regardless of examples chosen.

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	COMMENTS	`All examples are Bongard Problems fitting left or right in BP793.` `All examples here are in the conventional format, i.e. white background, black vertical dividing line, and examples in boxes on either side.` `Border cases are Bongard Problems that always self-sort one way given their particular visual format (e.g. fixed number of boxes), but self-sort a different way in another slightly different format.` `Meta Bongard Problems appearing in BP793 that are presentationinvariant necessarily fit right here.` `It is interesting to think about how this Bongard Problem sorts itself. The only self-consistent answer is that it fits right.`
	CROSSREFS	`See BP793 "sorts self left vs. sorts self right".` `See BP944 "sorts every BP on one side vs. doesn't".` `Adjacent-numbered pages: BP922 BP923 BP924 BP925 BP926 * BP928 BP929 BP930 BP931 BP932`
	KEYWORD	`hard, solved, presentationinvariant, visualimagination`
	WORLD	`boxes_bpimage_sorts_self [smaller \| same \| bigger] zoom in left (boxes_bpimage_sorts_self_incarnation_dependent) \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

BP944

Image of Bongard Problem that would sort ANY image of a valid Bongard Problem on one of its sides vs. image of Bongard Problem whose categorization of a BP image would depend on the solution or examples in it.

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	COMMENTS	`"Any" here means any image of a Bongard Problem in the relevant format, i.e. with white background, black vertical dividing line, and examples in boxes on either side.` `All examples shown in this Problem clearly sort themselves on the left or right.` `A self-referential but maybe simpler solution is "would sort all examples in this whole Bongard Problem on one of its sides vs. not so." Users adding examples please try to maintain this: for any example you add to the right of this Bongard Problem, make sure it does not sort all the other examples in this Bongard Problem on just one of its sides. - Aaron David Fairbanks, Aug 26 2020`
	CROSSREFS	`Adjacent-numbered pages: BP939 BP940 BP941 BP942 BP943 * BP945 BP946 BP947 BP948 BP949`
	KEYWORD	`hard, challenge, presentationinvariant`
	WORLD	`boxes_bpimage_sorts_self [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Jago Collins`

BP952

Images of Bongard Problems about images of Bongard Problems about images of Bongard Problems vs. images of Bongard Problems not including images of Bongard Problems including images of Bongard Problems.

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	CROSSREFS	`See BP547 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).` `Any left example in this BP will be a left example for BP1084.` `Adjacent-numbered pages: BP947 BP948 BP949 BP950 BP951 * BP953 BP954 BP955 BP956 BP957`
	KEYWORD	`meta (see left/right), miniproblems, funny, presentationinvariant`
	CONCEPT	`recursion (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left`
	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`

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