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BP1 Empty image vs. non-empty image.
(edit; present; nest [left/right]; search; history)
COMMENTS

The first Bongard Problem.

All examples in this Bongard Problem are line drawings (one or more connected figures made up of curved and non-curved lines).

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.

CROSSREFS

Adjacent-numbered pages:
  *  BP2 BP3 BP4 BP5 BP6

EXAMPLE

A circle fits on the right because it is not nothing.

KEYWORD

easy, nice, precise, allsorted, unstable, world, left-narrow, left-finite, left-full, left-null, perfect, pixelperfect, finished, traditional, stableworld, deformstable, bongard

CONCEPT empty (info | search),
existence (info | search),
zero (info | search)

WORLD

zoom in left (blank_image) | zoom in right (curves_drawing)

AUTHOR

Mikhail M. Bongard

BP211 More black than white vs. more white than black.
(edit; present; nest [left/right]; search; history)
CROSSREFS

See BP196 for a version of this Problem restricted to uniform textures.

Adjacent-numbered pages:
BP206 BP207 BP208 BP209 BP210  *  BP212 BP213 BP214 BP215 BP216

KEYWORD

easy, nice, spectrum, dual, blackwhite, unstable, right-null, perfect, pixelperfect, traditional, continuous, viceversa, bordercontent

CONCEPT outlined_filled (info | search),
size (info | search),
texture (info | search)

WORLD

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

AUTHOR

Giuseppe Insana

BP359 Random arrangement of pixels vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

By "random" we mean it's reasonable to expect each pixel in the image was chosen with a constant, consistent chance of being black or white.

CROSSREFS

Adjacent-numbered pages:
BP354 BP355 BP356 BP357 BP358  *  BP360 BP361 BP362 BP363 BP364

KEYWORD

nice, right-narrow, collective, experimental, blackwhiteinvariant

CONCEPT pattern_or_random (info | search)

WORLD

bmp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP374 Simple object vs. complex object.
(edit; present; nest [left/right]; search; history)
COMMENTS

People consistently get the answer to this, but many people think they haven't found the actual answer yet even though they have. - Aaron David Fairbanks, Aug 16 2020

CROSSREFS

Adjacent-numbered pages:
BP369 BP370 BP371 BP372 BP373  *  BP375 BP376 BP377 BP378 BP379

KEYWORD

easy, nice, traditional

CONCEPT simplicity (info | search)

AUTHOR

Aaron David Fairbanks

BP533 Contains smaller copy of itself vs. doesn't.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP528 BP529 BP530 BP531 BP532  *  BP534 BP535 BP536 BP537 BP538

EXAMPLE

A smaller copy of EX6409 (the black area) can be located within itself, but some of the white space inside it is not retained in this smaller copy.

KEYWORD

perfect, infinitedetail, contributepairs

CONCEPT fractal (info | search),
recursion (info | search),
self-reference (info | search)

WORLD

connected_built_from_self_tile_fractals [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP961 Includes itself on the left vs. includes itself on the right.
(edit; present; nest [left/right]; search; history)
COMMENTS

Some examples are Bongard Problems with this solution.

CROSSREFS

Adjacent-numbered pages:
BP956 BP957 BP958 BP959 BP960  *  BP962 BP963 BP964 BP965 BP966

KEYWORD

nice, precise, dual, handed, leftright, perfect, infinitedetail, both, neither, preciseworld

CONCEPT fractal (info | search),
recursion (info | search),
self-reference (info | search)

AUTHOR

Aaron David Fairbanks

BP979 It is possible to deduce the contents of the missing square vs. not so.
?
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples show grids of squares with an image in each square, such that there is some "rule" the images within the grid obey. The "rule" can be about how the images relate to their neighbors, it can involve the position of the images in the grid, and it can involve properties of the grid considered as a whole. One square from somewhere along the edge of the grid is removed.


Intentionally left out of this Problem (shown above sorted ambiguously) are cases in which the rule is not possible to deduce without seeing more squares. Due to this choice to omit those kinds of examples from the right, another acceptable solution is "it is possible to deduce the contents of the missing square once the underlying rule is understood vs. not so."

REFERENCE

https://en.wikipedia.org/wiki/Raven%27s_Progressive_Matrices

CROSSREFS

BP1258 is very similar: whether ALL squares can be deduced from the rest.

Adjacent-numbered pages:
BP974 BP975 BP976 BP977 BP978  *  BP980 BP981 BP982 BP983 BP984

KEYWORD

nice, notso, structure, rules, miniworlds

CONCEPT convey_enough_information (info | search),
choice (info | search)

WORLD

grid_of_images_with_rule_one_on_edge_missing [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1206 Vertical axis of symmetry vs. no vertical axis of symmetry.
(edit; present; nest [left/right]; search; history)
COMMENTS

The solution for this Bongard Problem is also a (less specific) solution for BP500, "vertical axis of symmetry vs. no axis of symmetry".

CROSSREFS

BP1207 is the same solution but using the horizontal axis instead of the vertical axis.

BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.

Adjacent-numbered pages:
BP1201 BP1202 BP1203 BP1204 BP1205  *  BP1207 BP1208 BP1209 BP1210 BP1211

KEYWORD

stub, notso, stretch, left-narrow, traditional

CONCEPT symmetry_axis (info | search),
symmetry (info | search),
vertical (info | search)

AUTHOR

Aaron David Fairbanks

BP1208 More triangles left than right vs. more triangles right than left.
(edit; present; nest [left/right]; search; history)
COMMENTS

The triangles vary in size in order to make the solution clearly about quantity, not "total mass".

CROSSREFS

Adjacent-numbered pages:
BP1203 BP1204 BP1205 BP1206 BP1207  *  BP1209 BP1210 BP1211 BP1212 BP1213

KEYWORD

stub, precise, spectrum, dual, handed, leftright, traditional

CONCEPT number (info | search),
triangle (info | search),
quantity_comparison (info | search)

AUTHOR

Aaron David Fairbanks

BP1209 Empty square present vs. no square present.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Nearly identical to BP1221, which is the same except non-empty squares are allowed.

See BP24 for "circle present vs. not".

Adjacent-numbered pages:
BP1204 BP1205 BP1206 BP1207 BP1208  *  BP1210 BP1211 BP1212 BP1213 BP1214

KEYWORD

stub, left-narrow, traditional

CONCEPT empty (info | search),
existence (info | search),
square (info | search)

AUTHOR

Aaron David Fairbanks

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