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`

BP843

Lower bound is object vs. lower bound is nothing.

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	CROSSREFS	`Adjacent-numbered pages: BP838 BP839 BP840 BP841 BP842 * BP844 BP845 BP846 BP847 BP848`
	KEYWORD	`creativeexamples, structure, rules`
	CONCEPT	`empty (info \| search)`
	WORLD	`constant_change_seq_increase_right_lower_bound [smaller \| same \| bigger] zoom in left (constant_change_seq_increase_right_low_bound_obj)`
	AUTHOR	`Aaron David Fairbanks`

BP845

"Noisy" properties changing independent of the consistently increasing quantity vs. not so.

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	COMMENTS	`"Noisy" sequences of change vs. "minimalist" sequences of change.`
	CROSSREFS	`See BP511 for noise in BPs.` `See BP827 for noise in images of BPs.` `Adjacent-numbered pages: BP840 BP841 BP842 BP843 BP844 * BP846 BP847 BP848 BP849 BP850`
	KEYWORD	`creativeexamples, structure, contributepairs, rules`
	WORLD	`quantity_change_seq_increase_right_noise_allowed [smaller \| same \| bigger] zoom in right (quantity_change_seq_increase_right)`
	AUTHOR	`Aaron David Fairbanks`

BP846

A quantity increases by fixed constant amount each step vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP841 BP842 BP843 BP844 BP845 * BP847 BP848 BP849 BP850 BP851`
	KEYWORD	`creativeexamples, structure, contributepairs, rules`
	WORLD	`quantity_change_seq_increase_right [smaller \| same \| bigger] zoom in right (constant_change_seq_increase_right)`
	AUTHOR	`Aaron David Fairbanks`

BP848

Lower bound object shown vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP843 BP844 BP845 BP846 BP847 * BP849 BP850 BP851 BP852 BP853`
	KEYWORD	`creativeexamples, structure, contributepairs, rules`
	WORLD	`constant_change_seq_increase_right_low_bound_obj [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP852

Object shown below is the "limit" of the sequence above (end result after "infinite time") versus not so.

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	COMMENTS	`The conceptual limit of the sequence may not be the limit of the points in the image. For example in a sequence of halvings the limit value is never reached, so the bottom would never change color and thus its limit would not would not either.` `Sequences progress from left to right (and there is not usually a way to intuitively extend the sequence in the other direction).`
	CROSSREFS	`Adjacent-numbered pages: BP847 BP848 BP849 BP850 BP851 * BP853 BP854 BP855 BP856 BP857`
	KEYWORD	`notso, creativeexamples, perfect, infinitedetail, assumesfamiliarity, structure, contributepairs, rules`
	AUTHOR	`Aaron David Fairbanks`

BP855

Object below ambiguously sorted (not clearly left or right) by Bongard Problem image above vs. object below clearly sorted by Bongard Problem image above.

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

	COMMENTS	`Represented are Bongard Problems and an extra object to sort, a.k.a. the Bongard's Dozen format.` `A variety of kinds of ambiguities showcased as left examples.`
	CROSSREFS	`Adjacent-numbered pages: BP850 BP851 BP852 BP853 BP854 * BP856 BP857 BP858 BP859 BP860`
	KEYWORD	`nice, creativeexamples, structure, rules`
	WORLD	`bdimage_shapes_extra_below [smaller \| same \| bigger] zoom in right (bdimage_shapes_extra_below_clear_sort)`
	AUTHOR	`Aaron David Fairbanks`

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