Adjacent-numbered pages:
BP849 BP850 BP851 BP852 BP853  *  BP855 BP856 BP857 BP858 BP859

left-finite, right-finite, left-full, right-full, finished, experimental, funny

nothing [same | bigger]
zoom in left (nothing) | zoom in right (nothing)

Aaron David Fairbanks

This is the "smallest" possible valid Bongard Problem on black and white bitmap images (up to switching sides).

Adjacent-numbered pages:
BP854 BP855 BP856 BP857 BP858  *  BP860 BP861 BP862 BP863 BP864

minimal, blackwhite, perfect, pixelperfect, experimental, funny, unstableworld

black_or_white_pixel [smaller | same | bigger]
zoom in left (black_pixel) | zoom in right (white_pixel)

Aaron David Fairbanks

A spot-the-difference exercise.

Arguably invalid (solution not simple).

Adjacent-numbered pages:
BP915 BP916 BP917 BP918 BP919  *  BP921 BP922 BP923 BP924 BP925

less, precise, convoluted, arbitrary, stretch, unstable, left-finite, left-full, perfect, pixelperfect, experimental, funny

bmp [smaller | same | bigger]

Aaron David Fairbanks

Evidently this solution is stretching the idea of what makes images "different". Each corresponding pair of panels would be parsed as identical in any other case. It is worth noting that if you view this Problem on a template, the solution no longer applies at all.

Adjacent-numbered pages:
BP936 BP937 BP938 BP939 BP940  *  BP942 BP943 BP944 BP945 BP946

less, precise, dual, antihuman, contributepairs, invalid, experimental, funny

Leo Crabbe

Right:

All are "all but one are ___"; all but one are black.

All are "every other is ___"; every other is solid polygons.

All are "gradually becoming ___"; gradually becoming thickly outlined.

Left:

All but one are "all but one are ___".

Every other is "every other is ___".

Gradually becoming "gradually becoming ___".

Here is another way of putting it:

Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.

Here is a more belabored way of putting it:

Call something like "is star-shaped" a "rule". An object can fit a rule.

Call something like "all but one are ___" a "rule-parametrized rule". A collection of objects, with respect to a particular rule, can fit a rule-parametrized rule.

A drawing on the right shows many collections. Every collection fits the same rule-parametrized rule (with respect to various rules); furthermore the collection of collections fits that same rule-parametrized rule (with respect to some rule collections can fit).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring rule-parametrized rule. The collection of collections must fit that rule-parametrized rule with respect to the rule of fitting that rule-parametrized rule (with respect to various rule).

An unintended solution to this BP is "not all groups share some noticeable property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the rule-parametrized rule usually has to do with not all objects in the collection fitting the rule. (See BP568, which is about BP ideas that are always overridden by a simpler solution.)

Some examples would fit left under a certain interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). But those rules are not necessarily the most obvious ways of interpreting these pictures, so they have been marked as ambiguous. Either of these placed on the left would prevent the intended solution being overridden (see the previous paragraph).

Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

The right side of this Problem is a subset of BP999^left.

Adjacent-numbered pages:
BP993 BP994 BP995 BP996 BP997  *  BP999 BP1000 BP1001 BP1002 BP1003

"Odd one out with respect to what property is the odd one out" would not fit left in this Problem: even though this example does seem doubly-meta, it is not doubly-meta in the right way. There is no odd one out with respect to the property of having an odd one out.

Similarly, consider "gradual transition with respect to what the gradual transition is between", etc. Instead of having the form "X 'X __' ", this is more like "X [the __ appearing in 'X __'] ". Examples like these two could make for a different Bongard Problem.

hard, unwordable, challenge, overriddensolution, infodense, contributepairs, funny, rules, miniworlds

zoom in right

Aaron David Fairbanks