Every Bongard Problem on the left shows invariance under some transformation in left sub-examples.

Some Bongard Problems on the right are symmetrical or have sub-examples that are symmetrical.

See BP760 for the version with links to pages on the OEBP instead of images of Bongard Problems.

Adjacent-numbered pages:
BP831 BP832 BP833 BP834 BP835  *  BP837 BP838 BP839 BP840 BP841

meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

boxes_bpimage_three_per_side [smaller | same | bigger]

Aaron David Fairbanks

"Tiling" is placing shapes next to each other without overlap to fill up space or other shapes.

See BP706 for the version with links to pages on the OEBP instead of images of Bongard Problems.

Adjacent-numbered pages:
BP830 BP831 BP832 BP833 BP834  *  BP836 BP837 BP838 BP839 BP840

meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

boxes_bpimage_three_per_side [smaller | same | bigger]

Aaron David Fairbanks

When removal of a box changes the solution, it cannot remove the existing solution; it can only allow more possible new solutions. Conversely, adding boxes can only narrow down between existing solutions.

The special box is always placed in the bottom left for help, but another solution is "there is some box whose removal allows another solution vs. not".

Bongard Problems sorted left might be called "deceptive". Especially when the solution ruled out by the one box is the more obvious solution.

Adjacent-numbered pages:
BP829 BP830 BP831 BP832 BP833  *  BP835 BP836 BP837 BP838 BP839

meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure

boxes_bpimage_three_per_side [smaller | same | bigger]

Aaron David Fairbanks

All examples are "object present vs. object absent" Problems.

Adjacent-numbered pages:
BP828 BP829 BP830 BP831 BP832  *  BP834 BP835 BP836 BP837 BP838

abstract, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

[smaller | same | bigger]

Aaron David Fairbanks

"Specific object" we mean the same connected figure (up to movement around the box). It is ambiguous whether a scaled, rotated, or reflected version of an object would be considered "the same object" because no examples on either side are forced to deal with that subtlety in their respective solutions.

Adjacent-numbered pages:
BP827 BP828 BP829 BP830 BP831  *  BP833 BP834 BP835 BP836 BP837

meta (see left/right), miniproblems, assumesfamiliarity, structure, presentationinvariant

[smaller | same | bigger]

Aaron David Fairbanks

Right examples are Bongard Problems in which the left hand side is enough to communicate the full answer.

No examples shown have right side with multiple rules and left side narrowing down the answer.

Adjacent-numbered pages:
BP826 BP827 BP828 BP829 BP830  *  BP832 BP833 BP834 BP835 BP836

hard, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, contributepairs

boxes_bpimage_three_per_side [smaller | same | bigger]

Aaron David Fairbanks

Left: the left hand side is enough to communicate the answer; the left pattern can be seen without the counterexamples on the right.

Right: the right hand side is enough to communicate the answer; the right pattern can be seen without counterexamples on the left.

Flipping a BP will switch its sorting.

The following is taken from the comments on page BP513 (keyword left-narrow):

Call a pattern "narrow" if it is likely to be noticed in a collection of examples, without any counterexamples provided.

A collection of triangles will be recognized as such; "triangles" is a narrow pattern. A collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

See keywords left-narrow and right-narrow.

Adjacent-numbered pages:
BP825 BP826 BP827 BP828 BP829  *  BP831 BP832 BP833 BP834 BP835

dual, handed, leftright, meta (see left/right), miniproblems, contributepairs, viceversa, presentationinvariant

boxes_bpimage_three_per_side [smaller | same | bigger]

Aaron David Fairbanks

Left examples have no solution, but they do not break the rules in ways so extreme that it is plainly impossible for them to have a solution, such as including the same image on both sides or including no images per side. (See such as including the same image on both sides or including no images per side.

See BP522 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

See BP968 (flipped) for a version of this Bongard Problem including examples of invalid Bongard Problems that don't even admit a convoluted solution (the same image appears on both sides).

Also see BP1080, which is similar to BP968, but including various different formats of Bongard Problems, distinguishing them from arbitrary images that are not Bongard Problems.

Adjacent-numbered pages:
BP824 BP825 BP826 BP827 BP828  *  BP830 BP831 BP832 BP833 BP834

nice, meta (see left/right), miniproblems, creativeexamples, left-unknowable, right-narrow, assumesfamiliarity, structure, help, presentationinvariant

boxes_bpimage_three_per_side_nosoln_allowed [smaller | same | bigger]
zoom in right (boxes_bpimage_three_per_side)

Aaron David Fairbanks

Properties are considered independent if none logically implies the other (or its opposite).

Another way of putting it is that on the right, the most descriptive good solution is of the form "[property 1] AND [property 2] vs. neither".

Adjacent-numbered pages:
BP823 BP824 BP825 BP826 BP827  *  BP829 BP830 BP831 BP832 BP833

nice, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure

boxes_bpimage_three_per_side [smaller | same | bigger]

Aaron David Fairbanks

"Noise" is a property that changes between examples which is independent to the solution property.

See BP511 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

See BP845 for noise in sequences of quantity increase.

Adjacent-numbered pages:
BP822 BP823 BP824 BP825 BP826  *  BP828 BP829 BP830 BP831 BP832

nice, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, contributepairs

boxes_bpimage_three_per_side [smaller | same | bigger]

Aaron David Fairbanks