The On-Line Encyclopedia of Bongard Problems

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BP801

Number pointed to on number line is "important" mathematical constant vs. not so.

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	COMMENTS	`This is the "harder version" of BP505.`
	CROSSREFS	`Adjacent-numbered pages: BP796 BP797 BP798 BP799 BP800 * BP802 BP803 BP804 BP805 BP806`
	KEYWORD	`hard, less, abstract, math, subjective, challenge, right-unknowable, collective, experimental, finishedexamples`
	AUTHOR	`Aaron David Fairbanks`

BP825

Ticks mark an infinite sequence of angles on circle such that each angle is the double of the subsequent angle in the sequence (angle measured from rightmost indicated point) vs. not so.

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	COMMENTS	`This is solvable; it was solved by Sridhar Ramesh.` `A full turn is considered "the same angle" as no turns; likewise for adding and subtracting full turns from any angle. All sequences of angles shown start at the rightmost tick.` `It doesn't matter whether the angle is measured clockwise or counterclockwise, as long as the choice is consistent.`
	CROSSREFS	`Adjacent-numbered pages: BP820 BP821 BP822 BP823 BP824 * BP826 BP827 BP828 BP829 BP830`
	KEYWORD	`hard, convoluted, notso, math, solved`
	CONCEPT	`sequence (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP831

Image of a Bongard Problem with left side having two rules and right side narrowing it down vs. image of Bongard Problem whose right hand side adds no information.

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	COMMENTS	`Right examples are Bongard Problems in which the left hand side is enough to communicate the full answer.` `No examples shown have right side with multiple rules and left side narrowing down the answer.`
	CROSSREFS	`Adjacent-numbered pages: BP826 BP827 BP828 BP829 BP830 * BP832 BP833 BP834 BP835 BP836`
	KEYWORD	`hard, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, contributepairs`
	WORLD	`boxes_bpimage_three_per_side [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP842

Any permutation of positions that sends one string of symbols to another sends each string of symbols to some other versus not so.

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	COMMENTS	`Restriction of BP841 to permutations.`
	CROSSREFS	`Adjacent-numbered pages: BP837 BP838 BP839 BP840 BP841 * BP843 BP844 BP845 BP846 BP847`
	KEYWORD	`hard, contributepairs, traditional`
	CONCEPT	`permutation (info \| search)`
	WORLD	`zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

BP849

Loop is time-symmetrical (loop is like ABCBABCBA... instead of like ABCABCABC...) up to rotation of object vs. not so (neither up to rotation nor reflection).

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	CROSSREFS	`Adjacent-numbered pages: BP844 BP845 BP846 BP847 BP848 * BP850 BP851 BP852 BP853 BP854`
	KEYWORD	`hard, convoluted, solved, rules`
	WORLD	`constant_change_seq_loop_right [smaller \| same \| bigger]`
	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`

BP871

A reflection can switch an object's sorting vs. not so.

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	COMMENTS	`In particular, horizontal reflections work in all left examples.` `An image of this Bongard Problem would fit on the left.`
	CROSSREFS	`See BP552 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).` `Adjacent-numbered pages: BP866 BP867 BP868 BP869 BP870 * BP872 BP873 BP874 BP875 BP876`
	KEYWORD	`hard, abstract, challenge, meta (see left/right), miniproblems, creativeexamples, presentationmatters, infodense, assumesfamiliarity, structure`
	WORLD	`bpimage_shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP872

A rotation can switch an object's sorting vs. not so.

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	CROSSREFS	`See BP553 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).` `Adjacent-numbered pages: BP867 BP868 BP869 BP870 BP871 * BP873 BP874 BP875 BP876 BP877`
	KEYWORD	`hard, challenge, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure`
	WORLD	`bpimage_shapes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP875

Problem would sort all relevant examples vs. possible objects similar to those seen on both sides would have no clear sorting.

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	COMMENTS	`Left examples partition a pool of objects cleanly into two classes.`
	CROSSREFS	`See BP509 (keyword "allsorted") for the version with links to pages on the OEBP instead of images of Bongard Problems.` `The left side implies BP876^left.` `Adjacent-numbered pages: BP870 BP871 BP872 BP873 BP874 * BP876 BP877 BP878 BP879 BP880`
	KEYWORD	`hard, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`bpimage_shapes [smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

BP876

Precise sorting of potential examples vs. not so.

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	COMMENTS	`Left Bongard Problems do not have to sort all relevant examples; if they would leave some border cases unsorted, it just has to be clear precisely which examples those would be.` `Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.`
	CROSSREFS	`See BP508 for the version with links to pages on the OEBP instead of images of Bongard Problems.` `Adjacent-numbered pages: BP871 BP872 BP873 BP874 BP875 * BP877 BP878 BP879 BP880 BP881`
	KEYWORD	`hard, notso, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant`
	WORLD	`bpimage_shapes [smaller \| same \| bigger] zoom in left (bpimage_shapes_exact_sort)`
	AUTHOR	`Aaron David Fairbanks`

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