The On-Line Encyclopedia of Bongard Problems

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BP341

Strictly increasing or strictly decreasing border line vs. both increasing and decreasing border line.

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	CROSSREFS	`Adjacent-numbered pages: BP336 BP337 BP338 BP339 BP340 * BP342 BP343 BP344 BP345 BP346`
	KEYWORD	`math, perfect, pixelperfect, traditional`
	CONCEPT	`size_increase_decrease (info \| search),` `or (info \| search),` `outlined_filled (info \| search),` `tracing_line_or_curve (info \| search),` `texture (info \| search)`
	WORLD	`function_graph_black_below_white_above [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP344

Shape can tile itself vs. shape cannot tile itself.

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	COMMENTS	`Left examples are sometimes called "rep-tiles."` `The tiles all must be the same size. More specifically, all left examples can tile themselves only using scaled down and rotated versions of themselves with all tiles the same size. Right examples cannot tile themselves using scaled down rotated versions of themselves or even reflected versions of themselves with all tiles the same size.` `Without the puzzle piece-like shape EX4120 on the right side the current examples also allow the solution "shape can tile with itself so as to create a parallelogram vs. shape cannot tile with itself so as to create a parallelogram."`
	CROSSREFS	`See BP532 for a version with fractals.` `Adjacent-numbered pages: BP339 BP340 BP341 BP342 BP343 * BP345 BP346 BP347 BP348 BP349`
	EXAMPLE	`Go to https://oebp.org/files/yet.png for an illustration of how some left-sorted shapes tile themselves.`
	KEYWORD	`hard, precise, notso, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, traditional`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search),` `tiling (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`shape [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP369

All points (small white circles) on one figure can be glued together to make the other figure vs. not so.

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	CROSSREFS	`See BP851 for a version where the figure must stay within the 2D plane and cannot pass through itself while being deformed.` `Adjacent-numbered pages: BP364 BP365 BP366 BP367 BP368 * BP370 BP371 BP372 BP373 BP374`
	KEYWORD	`nice, math, traditional`
	CONCEPT	`topological_transformation (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	WORLD	`zoom in left (figure_made_of_curves_and_quotient_by_hollow_dots)`
	AUTHOR	`Aaron David Fairbanks`

BP370

Gluing sides with the same symbols makes a sphere vs. gluing sides with the same symbols makes a torus.

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	CROSSREFS	`Adjacent-numbered pages: BP365 BP366 BP367 BP368 BP369 * BP371 BP372 BP373 BP374 BP375`
	KEYWORD	`math`
	CONCEPT	`topological_transformation (info \| search),` `3d_solid (info \| search),` `imagined_motion (info \| search),` `motion (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP378

The two objects are conceptually related vs. the two objects are conceptually unrelated.

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	CROSSREFS	`See BP347, which is similar.` `Adjacent-numbered pages: BP373 BP374 BP375 BP376 BP377 * BP379 BP380 BP381 BP382 BP383`
	KEYWORD	`abstract, math, unorderedpair, traditional`
	CONCEPT	`same_concept (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP380

The completed version of the collection indicated by the objects is finite vs. the completed version of the collection indicated by the objects is infinite.

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	COMMENTS	`Related to BP870 and BP792.` `An example with clusters of perfect numbers of dots would be sorted ambiguously, for the time being. Unfortunately the 3rd smallest perfect number is 496. - Leo Crabbe, Oct 18 2024`
	CROSSREFS	`Adjacent-numbered pages: BP375 BP376 BP377 BP378 BP379 * BP381 BP382 BP383 BP384 BP385`
	KEYWORD	`math, creativeexamples, traditional, rules, miniworlds, collection`
	CONCEPT	`finite_infinite (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP381

Adding the top two waves yields the bottom wave vs. not so.

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	COMMENTS	`This problem is about wave interference.`
	CROSSREFS	`Adjacent-numbered pages: BP376 BP377 BP378 BP379 BP380 * BP382 BP383 BP384 BP385 BP386`
	KEYWORD	`nice, notso, math, orderedtriplet, traditional`
	CONCEPT	`addition (info \| search),` `wave (info \| search),` `2_inputs_1_output (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP382

No knot (unknot) vs. knot.

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	COMMENTS	`To hint at the solution, left examples can be arranged in a sequence to show the unknot tying itself.`
	CROSSREFS	`Adjacent-numbered pages: BP377 BP378 BP379 BP380 BP381 * BP383 BP384 BP385 BP386 BP387`
	KEYWORD	`nice, math, anticomputer, help, traditional`
	CONCEPT	`knot (info \| search),` `topological_transformation (info \| search)`
	WORLD	`knot [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP384

Square number of dots vs. non-square number of dots.

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	COMMENTS	`All examples in this Problem are a collection of dots.` `An equivalent solution is "Dots can be arranged into a square lattice whose convex hull is a square vs. not so". - Leo Crabbe, Aug 01 2020`
	CROSSREFS	`Adjacent-numbered pages: BP379 BP380 BP381 BP382 BP383 * BP385 BP386 BP387 BP388 BP389`
	EXAMPLE	`A single dot fits because 1 = 11.` `A pair of dots does not fit because there is no integer x such that 2 = xx.`
	KEYWORD	`nice, precise, allsorted, number, math, left-narrow, left-null, help, traditional, preciseworld, collection`
	CONCEPT	`square_number (info \| search)`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP505

Number indicated on number line conceptually related to image shown below vs. not so.

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	COMMENTS	`This is the "easier version" of BP801.` `All numbers on the left are canonical mathematical constants, i.e. there are no totally arbitrary ratios, with images below featuring those ratios.`
	CROSSREFS	`Adjacent-numbered pages: BP500 BP501 BP502 BP503 BP504 * BP506 BP507 BP508 BP509 BP510`
	KEYWORD	`fuzzy, math`
	CONCEPT	`number (info \| search),` `ratio (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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