Adjacent-numbered pages:
BP1044 BP1045 BP1046 BP1047 BP1048  *  BP1050 BP1051 BP1052 BP1053 BP1054

teach, creativeexamples, left-narrow, right-narrow, contributepairs, fixedgrid, miniworlds

Jago Collins

All examples in this Problem are solid concave black shapes. In this Problem, the "cavities" of a concave shape are defined to be the convex hull of the shape minus the shape itself. For example, if you take a bite out of the edge of a piece of paper, the piece of paper in your mouth is the cavity of the bitten piece of paper. The idea may be indefinitely extended, considering whether the cavities of the cavities are concave or convex, and so on.

Adjacent-numbered pages:
BP987 BP988 BP989 BP990 BP991  *  BP993 BP994 BP995 BP996 BP997

nice, precise, perfect, traditional

concave_fill_shape [smaller | same | bigger]

Jago Collins

All examples in this Problem are sequences of graphic symbols. In this Problem, a "palindrome" is taken to be an ordered sequence which is the same read left-to-right as it is read right-to-left. A more formal solution to this Problem could be: "Sequences which are invariant under a permutation which swaps first and last entries, second and second last entries, third and third last entries, ... and so on vs. sequences which are not invariant under the aforementioned permutamation."

Adjacent-numbered pages:
BP981 BP982 BP983 BP984 BP985  *  BP987 BP988 BP989 BP990 BP991

nice, precise, allsorted, notso, sequence, traditional

zoom in left | zoom in right

Jago Collins

Each example in this Bongard Problem consists of mini-panels containing the same arrangement of circles (ignoring colouring). Each mini-panel has a single circle highlighted in red, and possibly some circles highlighted in blue. A strict rule for this Bongard Problem could be something like "If a circle is blue in one mini-panel and red in a second mini-panel, then the red circle from the first mini-panel is blue in the second mini-panel." The relation intepretation is that a circle is related to the red circle if and only if it is coloured blue. BP973 is a similar problem.

Adjacent-numbered pages:
BP970 BP971 BP972 BP973 BP974  *  BP976 BP977 BP978 BP979 BP980

convoluted, color, infodense, rules

Jago Collins

Each example in this Bongard Problem consists of mini-panels containing the same arrangement of circles (ignoring colouring). Each mini-panel has a single circle highlighted in red, and possibly some circles highlighted in blue. A strict rule for this Bongard Problem could be something like "If a circle is blue in one mini-panel and red in a second mini-panel, then there are no blue circles in the second mini-panel that weren't already blue in the first mini-panel." The relation interpretation is that a circle is related to the red circle if and only if it is coloured blue.

Adjacent-numbered pages:
BP968 BP969 BP970 BP971 BP972  *  BP974 BP975 BP976 BP977 BP978

convoluted, color, infodense, rules

Jago Collins

"Any" here means any image of a Bongard Problem in the relevant format, i.e. with white background, black vertical dividing line, and examples in boxes on either side.

All examples shown in this Problem clearly sort themselves on the left or right.

A self-referential but maybe simpler solution is "would sort all examples in this whole Bongard Problem on one of its sides vs. not so." Users adding examples please try to maintain this: for any example you add to the right of this Bongard Problem, make sure it does not sort all the other examples in this Bongard Problem on just one of its sides. - Aaron David Fairbanks, Aug 26 2020

Adjacent-numbered pages:
BP939 BP940 BP941 BP942 BP943  *  BP945 BP946 BP947 BP948 BP949

hard, challenge, presentationinvariant

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

Jago Collins

All examples in this Problem are outlines of convex polygons.

This is a generalisation of scalene triangles to any polygon.

The left side implies the right side of BP329 (regular vs. irregular polygons), but the converse is not true.

The left side of BP329 implies the right side, but the converse is not true.

Adjacent-numbered pages:
BP919 BP920 BP921 BP922 BP923  *  BP925 BP926 BP927 BP928 BP929

Any scalene triangle will fit on the left, because no two sides are equal.

However, any regular polygon will not fit on the left, because all of its sides are equal.

A random convex polygon will "almost surely" fit on the left.

nice, stretch, right-narrow, traditional

polygon_outline [smaller | same | bigger]

Jago Collins

Adjacent-numbered pages:
BP910 BP911 BP912 BP913 BP914  *  BP916 BP917 BP918 BP919 BP920

less, notso, spectrum, number, example, left-null, impossible, experimental

dots [smaller | same | bigger]

Jago Collins

This Problem is related to the four colour theorem.

Adjacent-numbered pages:
BP894 BP895 BP896 BP897 BP898  *  BP900 BP901 BP902 BP903 BP904

hard, nice, math

[smaller | same | bigger]

Jago Collins

https://en.wikipedia.org/wiki/Stability_theory

Adjacent-numbered pages:
BP546 BP547 BP548 BP549 BP550  *  BP552 BP553 BP554 BP555 BP556

The classic example is a pendulum with a solid rod (instead of a string) which has a stable balance point at the bottom of its swing, where if you move the pendulum slightly it will swing back towards that balanced state. However, theoretically the pendulum can also be balanced pointing directly up. In this case, if you move the pendulum slightly it will swing down away from that upwards balanced state.

updown, rotate, physics, anticomputer, perfect

Jago Collins