Examples sorted right may feature multiple quantities, but one changing quantity determines all changing quantities.

The distinction between the two sides is fuzzy. For example the left-sorted example EX4364 could be viewed as determined by just the one changing quantity of width and the fact that the height is given by two times the width minus one. On the other hand the right-sorted example EX4370 could be viewed as determined by the two changing quantities number of black squares and number of white squares, ignoring the fact that the total number of squares is always six.

Adjacent-numbered pages:
BP360 BP361 BP362 BP363 BP364  *  BP366 BP367 BP368 BP369 BP370

fuzzy, traditional, rules, miniworlds

constant_change_seq_increase_right [smaller | same | bigger]

Aaron David Fairbanks

"True" vs. "false."

Adjacent-numbered pages:
BP388 BP389 BP390 BP391 BP392  *  BP394 BP395 BP396 BP397 BP398

nice, fuzzy, abstract, collective, contributepairs, traditional, rules, miniworlds, dithering

Jago Collins

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.

Adjacent-numbered pages:
BP500 BP501 BP502 BP503 BP504  *  BP506 BP507 BP508 BP509 BP510

fuzzy, math

Aaron David Fairbanks

All examples are black and white images, partitioned by lines such that crossing a line switches the background color and the foreground color. (Sometimes it is not clear which is "background" and which is "foreground".) In the space between two dividing lines, there is a black and white scene; the outlines of the shapes are curves dividing black from white. Images sorted left are such that each outline-curve present in a scene that comes in contact non-tangentially with a dividing line continues across the dividing line, across which the black and white sides of it switch.

Examples (especially right) usually have ambiguity to some degree; depending on how a person reads the images, dividing lines may be confused for curves within a scene.

Adjacent-numbered pages:
BP519 BP520 BP521 BP522 BP523  *  BP525 BP526 BP527 BP528 BP529

fuzzy, unwordable, anticomputer, traditional, blackwhiteinvariant

Aaron David Fairbanks

Adjacent-numbered pages:
BP807 BP808 BP809 BP810 BP811  *  BP813 BP814 BP815 BP816 BP817

easy, fuzzy, abstract, notso, stretch, anticomputer, subjective, invalid, experimental, funny, dithering

Aaron David Fairbanks

This is a very fuzzy definition. Some left examples arguably should be placed on the right, since the particular way they are represented is arbitrary--the Platonic solids EX6730 and primes EX6734 especially, as these show arbitrary placement and arrangement of objects. Furthermore if arbitrary representations are allowed one cannot be sure for example the right hand drawing of random numbers EX6740 does not represent "numbers" in general. Still this Bongard Problem has been solved by people.

Adjacent-numbered pages:
BP808 BP809 BP810 BP811 BP812  *  BP814 BP815 BP816 BP817 BP818

fuzzy, abstract, stretch, math, solved, collective, experimental, dithering

Aaron David Fairbanks

Or, perhaps more concretely, "Depiction of object with some symmetry (invariance under transformation) vs. depiction of object with no simple symmetries."

Adjacent-numbered pages:
BP842 BP843 BP844 BP845 BP846  *  BP848 BP849 BP850 BP851 BP852

nice, fuzzy, abstract, math, concept, collective, dithering

Leo Crabbe

One left and one right example with each solution are shown for help.

This BP is fuzzy for multiple reasons. How obvious it is that an example fits a rule is subjective. Also, somebody could read the simplicity of all included examples as part of a Bongard Problem's solution. For example, the more obvious version of "square number of dots vs. non-square number of dots" could be interpreted as "square small number of dots arranged in easy-to-read way vs. non-square small number of dots arranged in easy-to-read way."

Whether this Bongard Problem solution would categorize an image of itself left or right depends on the difficulty of the solutions of the mini-Problems.

See keyword help.

See keyword hardsort.

Adjacent-numbered pages:
BP889 BP890 BP891 BP892 BP893  *  BP895 BP896 BP897 BP898 BP899

fuzzy, abstract, notso, subjective, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, contributepairs

boxes_bpimage_three_per_side [smaller | same | bigger]

Aaron David Fairbanks

Panels on the left hand side contain geometrical objects that appear distorted (to a human) due to surrounding information.

Vicente Sierra-Vázquez & Ignacio Serrano-Pedraza, Application of Riesz transforms to the isotropic AM-PM decomposition of geometrical-optical illusion images, April 2010, Figure 1.

Adjacent-numbered pages:
BP934 BP935 BP936 BP937 BP938  *  BP940 BP941 BP942 BP943 BP944

fuzzy, anticomputer, subjective, contributepairs, invalid, experimental

Leo Crabbe

See BP1004 for a Problem about conceptual self-similarity instead of visual self-similarity.

See BP188 for a similar Problem restricted to shape outlines made of shape outlines.

Adjacent-numbered pages:
BP997 BP998 BP999 BP1000 BP1001  *  BP1003 BP1004 BP1005 BP1006 BP1007

easy, nice, fuzzy, abstract, anticomputer, concept, traditional

Aaron David Fairbanks