This refers to all Bongard Problem solution ideas. No need to be a particularly well-made or well-defined Bongard Problem.

Adjacent-numbered pages:
BP536 BP537 BP538 BP539 BP540  *  BP542 BP543 BP544 BP545 BP546

notso, meta (see left/right), links, world, left-self, right-null, left-it, feedback

everything [smaller | same]
zoom in left (bp)

Aaron David Fairbanks

Adjacent-numbered pages:
BP537 BP538 BP539 BP540 BP541  *  BP543 BP544 BP545 BP546 BP547

notso, meta (see left/right), links, oebp, world, left-self, right-null, left-it, feedback

everything [smaller | same]
zoom in left (bppage)

Aaron David Fairbanks

All ideas and things, with no limits.

Adjacent-numbered pages:
BP539 BP540 BP541 BP542 BP543  *  BP545 BP546 BP547 BP548 BP549

notso, meta (see left/right), links, world, left-self, right-finite, right-full, left-null, left-it, feedback, experimental, funny

everything [smaller | same]
zoom in left (everything) | zoom in right (nothing)

Aaron David Fairbanks

Left-sorted BPs have the keyword "notso" on the OEBP.

This meta Bongard Problem is about Bongard Problems featuring two rules that are conceptual opposites.

Sometimes both sides could be seen as the "not" side: consider, for example, two definitions of the same Bongard Problem, "shape has hole vs. does not" and "shape is not filled vs. is". It is possible (albeit perhaps unnatural) to phrase the solution either way when the left and right sides partition all possible relevant examples cleanly into two groups (see the allsorted keyword).

When one property is "positive-seeming" and its opposite is "negative-seeming", it usually means the positive property would be recognized without counter-examples (e.g. a collection of triangles will be seen as such), while the negative property wouldn't be recognized without counter-examples (e.g. a collection of "non-triangle shapes" will just be interpreted as "shapes" unless triangles are shown opposite them).

BP513 (keyword left-narrow) is about Bongard Problems whose left side can be recognized without the right side. When a Bongard Problem is left-narrow and not "right-narrow that usually makes the property on the left seem positive and the property on the right seem negative.

The OEBP by convention has preferred the "positive-seeming" property (when there is one) to be on the left side.

All in all, the keyword "notso" should mean:

1) If the Bongard Problem is "narrow" on at least one side, then it is left-narrow.

2) The right side is the conceptual negation of the left side.

If a Bongard Problem's solution is "[Property A] vs. not so", the "not so" side is everything without [Property A] within some suitable context. A Bongard Problem "triangles vs. not so" might only include simple shapes as non-triangles; it need not include images of boats as non-triangles. It is not necessary for all the kitchen sink to be thrown on the "not so" side (although it is here).

See BP1001 for a version sorting pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP. (This version is a little different. In BP1001, the kitchen sink of all other possible images is always included on the right "not so" side, rather than a context-dependent conceptual negation.)

Contrast keyword viceversa.

"[Property A] vs. not so" Bongard Problems are often allsorted, meaning they sort all relevant examples--but not always, because sometimes there exist ambiguous border cases, unclear whether they fit [Property A] or not.

Adjacent-numbered pages:
BP862 BP863 BP864 BP865 BP866  *  BP868 BP869 BP870 BP871 BP872

notso, meta (see left/right), links, keyword, left-self, funny

everything [smaller | same]
zoom in left

Aaron David Fairbanks

Although this Bongard Problem is self-referential, it's only because of the specific phrasing of the solution. "BP902 vs. anything else" would also work. The number 902 could have been chosen coincidentally.

See BP953, BP959.

Adjacent-numbered pages:
BP897 BP898 BP899 BP900 BP901  *  BP903 BP904 BP905 BP906 BP907

notso, meta (see left/right), links, left-self, left-narrow, left-finite, left-full, right-null, right-it, invalid, experimental, funny

everything [smaller | same]
zoom in left (bp902)

Leo Crabbe

In other words, we take the distance between points (a,b) and (c,d) to be equal to |c-a| + |d-b|, or, in other words, the distance of the shortest path between points that travels along grid lines. In mathematics, this way of measuring distance is called the 'taxicab' or 'Manhattan' metric. The points on the left hand side form equilateral triangles in this metric.

⠀

An alternate (albeit more convoluted) solution that someone may arrive at for this Problem is as follows: The triangles formed by the points on the left have some two points diagonal to each other (in the sense of bishops in chess), and considering the corresponding edge as their base, they also have an equal height. However, this was proven to be equivalent to the Manhattan distance answer by Sridhar Ramesh. Here is the proof:

⠀

An equilateral triangle amounts to points A, B, and C such that B and C lie on a circle of some radius centered at A, and the chord from B to C is as long as this radius.

A Manhattan circle of radius R is a turned square, ♢, where the Manhattan distance between any two points on opposite sides is 2R, and the Manhattan distance between any two points on adjacent sides is the larger distance from one of those points to the corner connecting those sides. Thus, to get two of these points to have Manhattan distance R, one of them must be a midpoint of one side of the ♢ (thus, bishop-diagonal from its center) and the other can then be any point on an adjacent side of the ♢ making an acute triangle with the aforementioned midpoint and center.

Adjacent-numbered pages:
BP929 BP930 BP931 BP932 BP933  *  BP935 BP936 BP937 BP938 BP939

hard, allsorted, solved, left-finite, right-finite, perfect, pixelperfect, unorderedtriplet, finishedexamples

3_dots_on_square_grid [smaller | same | bigger]

Leo Crabbe