The On-Line Encyclopedia of Bongard Problems

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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.

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	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.

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	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`

BP850

Shape can be maneuvered around the corner vs. not so.

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	REFERENCE	`https://en.wikipedia.org/wiki/Moving_sofa_problem`
	CROSSREFS	`Adjacent-numbered pages: BP845 BP846 BP847 BP848 BP849 * BP851 BP852 BP853 BP854 BP855`
	KEYWORD	`nice, precise, physics, creativeexamples, proofsrequired, left-narrow, right-narrow, dithering`
	CONCEPT	`rotation_required (info \| search),` `imagined_motion (info \| search),` `physically_fitting (info \| search)`
	AUTHOR	`Leo Crabbe`

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.

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	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`

BP860

Finitely many copies of the shape can be arranged such that they are locked together vs. not so.

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	CROSSREFS	`This is a generalisation of BP861.` `Adjacent-numbered pages: BP855 BP856 BP857 BP858 BP859 * BP861 BP862 BP863 BP864 BP865`
	KEYWORD	`hard, nice, stub, precise, stretch, unstable, hardsort, challenge, creativeexamples, perfect, pixelperfect`
	CONCEPT	`tiling (info \| search)`
	WORLD	`fill_shape [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP863

Two shapes can tessellate the plane together vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP858 BP859 BP860 BP861 BP862 * BP864 BP865 BP866 BP867 BP868`
	KEYWORD	`nice, precise, allsorted, math, hardsort, creativeexamples, unorderedpair`
	CONCEPT	`infinite_plane (info \| search),` `tessellation (info \| search),` `tiling (info \| search)`
	WORLD	`2_shapes [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP870

Increasing quantity has upper bound (will get "stopped" by something) vs. not so.

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	COMMENTS	`Related to BP380.`
	CROSSREFS	`Adjacent-numbered pages: BP865 BP866 BP867 BP868 BP869 * BP871 BP872 BP873 BP874 BP875`
	KEYWORD	`creativeexamples, structure, rules`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP893

As one quantity increases an equally obvious opposite quantity decreases vs. there is only one obvious quantity, which increases as the sequence progresses right.

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	COMMENTS	`Another way of phrasing the solution: "Neither direction would more naturally be called increase in quantity vs. rightward progression would be called an increase."` `Most right examples shown are unboundedly increasing, since finite sequences showing a quantity increasing usually also suggest "distance to end of sequence" as a decreasing opposite quantity. Even so, there are some finite sequences with one direction more intuitively increase-like than the other.`
	CROSSREFS	`Adjacent-numbered pages: BP888 BP889 BP890 BP891 BP892 * BP894 BP895 BP896 BP897 BP898`
	KEYWORD	`creativeexamples, structure, rules`
	WORLD	`constant_change_seq_increase_right [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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