Adjacent-numbered pages:
BP518 BP519 BP520 BP521 BP522  *  BP524 BP525 BP526 BP527 BP528

nice, precise, rotate, stretch, unstable, perfect, pixelperfect, traditional

shapes_can_touch_box [smaller | same | bigger]

Aaron David Fairbanks

Another solution is "evokes infinity vs. not so." Or "seen as having arbitrarily fine detail." All left examples show objects getting smaller and smaller and closer and closer together approaching some limit within the box.

Adjacent-numbered pages:
BP538 BP539 BP540 BP541 BP542  *  BP544 BP545 BP546 BP547 BP548

nice, abstract, concept, infinitedetail

Aaron David Fairbanks

All examples in this Problem are pairs of straight line segments.

This problem communicates the idea of projected distance, in this case from 2D to 1D (x-axis).

Adjacent-numbered pages:
BP552 BP553 BP554 BP555 BP556  *  BP558 BP559 BP560 BP561 BP562

nice, precise, allsorted, stretch, perfect, unorderedpair, preciseworld

two_segments [smaller | same | bigger]

Leo Crabbe

All examples in this Problem are groups of 3 dots.

Any example where 2 adjacent dots have the same height would be ambiguously sorted.

Adjacent-numbered pages:
BP553 BP554 BP555 BP556 BP557  *  BP559 BP560 BP561 BP562 BP563

Reading from right to left in the first box on the left hand side: the 2nd dot is higher than the 1st, and the 3rd is higher than the 2nd, so the sequence of dots is strictly increasing in height.

nice, precise, antihuman, orderedtriplet, preciseworld

three_points [smaller | same | bigger]

Leo Crabbe

If a "string" is wound tightly around the shape, does one of its segments lie directly on the shape?

All examples in this Problem are connected line segments or curves.

We are taking lines here to be infinitely thin, so that if the boundary of the convex hull intersects the endpoint of a line exactly it is understood that they meet at 1 point.

Adjacent-numbered pages:
BP559 BP560 BP561 BP562 BP563  *  BP565 BP566 BP567 BP568 BP569

Imagine wrapping a string around the pointed star. This string would take the shape of the boundary of the star's convex hull (a regular pentagon), and would only touch the star at the end of each of its 5 individual tips, therefore the star belongs on the left.

hard, nice, allsorted, solved, perfect

Leo Crabbe

All examples in this Problem are groups of black dots.

The nth triangular number is the sum over the natural numbers from 1 to n, where n > 0. Note: 0 is the 0th triangular number. The first few triangular numbers are 0, 1, 3 (= 1+2) and 6 (= 1+2+3)

Adjacent-numbered pages:
BP564 BP565 BP566 BP567 BP568  *  BP570 BP571 BP572 BP573 BP574

nice, precise, allsorted, notso, number, math, left-narrow, left-null, help, preciseworld

dots [smaller | same | bigger]

Leo Crabbe

Adjacent-numbered pages:
BP783 BP784 BP785 BP786 BP787  *  BP789 BP790 BP791 BP792 BP793

nice, precise, allsorted, math, traditional, preciseworld

connected_graph [smaller | same | bigger]

Aaron David Fairbanks

Rhetorical question: Where does this Bongard Problem sort an image of itself?

See BP999 and BP1004 for similar paradoxes.

Bongard Problems fitting left here evidently come in three categories: 1) would sort all Bongard Problems with the same solution left, 2) would sort all Bongard Problems with the same solution right, or 3) would sort some Bongard Problems with the same solution left and some right. See BP927.

See BP517 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

See BP954, which is about Bongard Problems not only sorting themselves, but moreover fractally appearing in themselves as panels.

Adjacent-numbered pages:
BP788 BP789 BP790 BP791 BP792  *  BP794 BP795 BP796 BP797 BP798

hard, nice, abstract, dual, handed, leftright, solved, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, experimental

boxes_bpimage_sorts_self [smaller | same | bigger]
zoom in left (boxes_bpimage_sorts_self_left) | zoom in right (boxes_bpimage_sorts_self_right)

Aaron David Fairbanks

"BONGARD HELL."

This the flipped version of BP793 but using only images of Bongard Problems with solution "__ half more black/less white than other half versus vice versa," that all use rotated, reflected, and inverted versions of the same examples.

See BP971 (left vs. right more black) and BP972 (top vs. bottom more black).

Adjacent-numbered pages:
BP790 BP791 BP792 BP793 BP794  *  BP796 BP797 BP798 BP799 BP800

hard, nice, abstract, dual, handed, leftright, meta (see left/right), miniproblems, presentationmatters, left-finite, right-finite, assumesfamiliarity, structure, experimental, funny

bongard_hell [smaller | same | bigger]
zoom in left | zoom in right

Aaron David Fairbanks

See BP567 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

Adjacent-numbered pages:
BP791 BP792 BP793 BP794 BP795  *  BP797 BP798 BP799 BP800 BP801

hard, nice, abstract, dual, handed, leftright, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

boxes_bpimage [smaller | same | bigger]

Aaron David Fairbanks