The On-Line Encyclopedia of Bongard Problems

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BP904

Rows show all possible ways a certain number of dots can be divided between a certain number of bins vs. not so.

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

	COMMENTS	`The rows in the panels on the right hand side show all the ways you can divide a certain number of dots between a certain number of bins, ignoring which bins they are placed in.`
	CROSSREFS	`Adjacent-numbered pages: BP899 BP900 BP901 BP902 BP903 * BP905 BP906 BP907 BP908 BP909`
	KEYWORD	`solved, left-null, grid, left-listable, right-listable`
	CONCEPT	`permutation (info \| search)`
	AUTHOR	`Molly C Klenzak`

BP903

Sharp vs. blurry

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

	CROSSREFS	`Adjacent-numbered pages: BP898 BP899 BP900 BP901 BP902 * BP904 BP905 BP906 BP907 BP908`
	KEYWORD	`contributepairs`
	CONCEPT	`contrast (info \| search),` `curve_texture (info \| search)`
	AUTHOR	`Cameron Fetter`

BP900

Black shape is a valid shadow (2D projection) of 3D shape vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP895 BP896 BP897 BP898 BP899 * BP901 BP902 BP903 BP904 BP905`
	KEYWORD	`3d, orderedpair`
	CONCEPT	`3d_solid (info \| search),` `projection (info \| search)`
	AUTHOR	`Leo Crabbe`

BP899

Regions in drawing (ignore background) can be coloured using three or fewer colours such that no adjacent regions are coloured the same colour vs. four colours are required.

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

	COMMENTS	`This Problem is related to the four colour theorem.`
	CROSSREFS	`Adjacent-numbered pages: BP894 BP895 BP896 BP897 BP898 * BP900 BP901 BP902 BP903 BP904`
	KEYWORD	`hard, nice, math`
	CONCEPT	`separated_regions (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP898

Can fold into tetragonal disphenoid ("isosceles tetrahedron") vs. cannot.

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

	COMMENTS	`Which two sides are the long sides and which side is the short side, or equivalently which angles are the wider angles and which angle is the narrower angle, is the only relevant information to consider for each triangle. Triangles are all assumed isosceles and congruent to one another.` `All examples in this Problem feature four of these triangles connected by corners and/or edges.`
	CROSSREFS	`BP897 was conceived as a false solution for this.` `Adjacent-numbered pages: BP893 BP894 BP895 BP896 BP897 * BP899 BP900 BP901 BP902 BP903`
	KEYWORD	`hard, precise, allsorted, notso, math, preciseworld`
	CONCEPT	`triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Molly C Klenzak`

BP897

Wide angles connected to narrow angles vs. not so.

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

	COMMENTS	`Another solution is that right examples can be folded down flat onto one isosceles triangle while left examples cannot.` `All examples in this Problem feature four isosceles triangles connected by corners and/or edges.`
	CROSSREFS	`This was conceived as a false solution for BP898.` `Adjacent-numbered pages: BP892 BP893 BP894 BP895 BP896 * BP898 BP899 BP900 BP901 BP902`
	KEYWORD	`precise, allsorted, notso, traditional, preciseworld`
	CONCEPT	`triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Molly C Klenzak, Aaron David Fairbanks`

BP896

Filled completely by fluid poured into gap (assuming there is already air) vs. not so.

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

	COMMENTS	`For a non-physics-based solution, "there exists a never-vertically-increasing path starting from the opening to each point in the interior vs. not so." - Aaron David Fairbanks, Aug 01 2020`
	CROSSREFS	`Adjacent-numbered pages: BP891 BP892 BP893 BP894 BP895 * BP897 BP898 BP899 BP900 BP901`
	KEYWORD	`nice, handed, updown, physics`
	CONCEPT	`liquid_flow (info \| search),` `gravity (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Zane Fry`

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.

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

	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`

BP892

Black shapes can be arranged such that they fit inside rectangular outline vs. not so.

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

	COMMENTS	`There is a slight ambiguity here regarding whether a shape could be placed within another shape's hole. This is a question of how one perceives the Problem: are we sliding shapes around on a table in 2D or are we allowed to 'lift' them in 3D space?`
	CROSSREFS	`Adjacent-numbered pages: BP887 BP888 BP889 BP890 BP891 * BP893 BP894 BP895 BP896 BP897`
	KEYWORD	`nice, precise, perfect, pixelperfect, help`
	CONCEPT	`rotation_required (info \| search),` `physically_fitting (info \| search)`
	AUTHOR	`Leo Crabbe`

BP891

Dots can be connected to create one triangle within another vs. not so.

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

	COMMENTS	`Or equivalently, "3 dots within boundary of convex hull vs. not so". - Leo Crabbe, Aug 01 2020`
	CROSSREFS	`Adjacent-numbered pages: BP886 BP887 BP888 BP889 BP890 * BP892 BP893 BP894 BP895 BP896`
	KEYWORD	`nice, precise, allsorted, preciseworld`
	CONCEPT	`convex_hull (info \| search),` `triangle (info \| search)`
	WORLD	`6_dots [smaller \| same \| bigger]`
	AUTHOR	`Cameron Fetter`

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