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

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 solid black shapes.

This problem is absurdly hard. It makes a good extreme example. - Aaron David Fairbanks, Nov 23 2020

Adjacent-numbered pages:
BP554 BP555 BP556 BP557 BP558  *  BP560 BP561 BP562 BP563 BP564

hard, nice, precise, allsorted, notso, stretch, challenge, left-narrow, perfect

fill_shape [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

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