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BP91 Three identical elements vs. four identical elements.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 244.

CROSSREFS

BP1226 is "three identical elements vs. other number of identical elements".

Adjacent-numbered pages:
BP86 BP87 BP88 BP89 BP90  *  BP92 BP93 BP94 BP95 BP96

KEYWORD

number, ignoreimperfections, finished, traditional, bongard

CONCEPT indentation (info | search),
on_line_or_curve (info | search),
number (info | search),
protrusion (info | search),
separation_of_joined_objects (info | search),
same (info | search),
three (info | search),
four (info | search)

WORLD

curves_and_fill_shapes_drawing [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP92 The chain does not branch vs. the chain branches.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 244.

CROSSREFS

Adjacent-numbered pages:
BP87 BP88 BP89 BP90 BP91  *  BP93 BP94 BP95 BP96 BP97

KEYWORD

finished, traditional, bongard

CONCEPT all (info | search),
branch_point (info | search),
collinear (info | search),
existence (info | search)

AUTHOR

Mikhail M. Bongard

BP93 Branches at outlined circle vs. branches at solid dark circle.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 244.

CROSSREFS

Adjacent-numbered pages:
BP88 BP89 BP90 BP91 BP92  *  BP94 BP95 BP96 BP97 BP98

KEYWORD

finished, traditional, bongard

CONCEPT branch_point (info | search),
collinear (info | search),
outlined_filled (info | search),
texture (info | search)

AUTHOR

Mikhail M. Bongard

BP94 Solid dark circle not at end vs. solid dark circle at end.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 245.

CROSSREFS

Adjacent-numbered pages:
BP89 BP90 BP91 BP92 BP93  *  BP95 BP96 BP97 BP98 BP99

KEYWORD

finished, traditional, bongard

CONCEPT between (info | search),
collinear (info | search),
line_or_curve_endpoint (info | search),
outlined_filled (info | search),
separation_of_joined_objects (info | search),
texture (info | search)

AUTHOR

Mikhail M. Bongard

BP95 Vertical hatched lines vs. horizontal hatched lines.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 245.

CROSSREFS

Adjacent-numbered pages:
BP90 BP91 BP92 BP93 BP94  *  BP96 BP97 BP98 BP99 BP100

KEYWORD

dual, rotate, finished, traditional, bongard

CONCEPT horizontal (info | search),
texture_area (info | search),
texture (info | search),
vertical (info | search)

AUTHOR

Mikhail M. Bongard

BP96 Triangles vs. quadrangles.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 245.

CROSSREFS

Adjacent-numbered pages:
BP91 BP92 BP93 BP94 BP95  *  BP97 BP98 BP99 BP100 BP101

KEYWORD

number, finished, traditional, bongard

CONCEPT collinear (info | search),
line_or_curve_endpoint (info | search),
number (info | search),
imagined_shape (info | search),
imagined_entity (info | search)

AUTHOR

Mikhail M. Bongard

BP97 Triangles vs. circles.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 246.

CROSSREFS

Adjacent-numbered pages:
BP92 BP93 BP94 BP95 BP96  *  BP98 BP99 BP100 BP101 BP102

KEYWORD

easy, nice, finished, traditional, bongard

CONCEPT convex_hull (info | search),
imagined_shape (info | search),
imagined_entity (info | search)

AUTHOR

Mikhail M. Bongard

BP98 Triangles vs. quadrangles.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 246.

CROSSREFS

Adjacent-numbered pages:
BP93 BP94 BP95 BP96 BP97  *  BP99 BP100 BP101 BP102 BP103

KEYWORD

easy, nice, noisy, number, finished, traditional, bongard

CONCEPT number (info | search)

AUTHOR

Mikhail M. Bongard

BP99 Outlines made by triangles and circles intersect vs. outlines made by triangles and circles do not intersect.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 246.

CROSSREFS

Adjacent-numbered pages:
BP94 BP95 BP96 BP97 BP98  *  BP100 BP101 BP102 BP103 BP104

KEYWORD

finished, traditional, bongard

CONCEPT collinear (info | search),
x-crossing (info | search),
cluster (info | search)

AUTHOR

Mikhail M. Bongard

BP100 The letter A vs. the letter Б.
(edit; present; nest [left/right]; search; history)
COMMENTS

This is the final problem in Bongard's original collection. It is the only member of the collection that makes reference to human culture. This can be interpreted symbolically as foreshadowing that computers will be able to perform the various tasks that humans can do.


Another idea introduced by this Bongard Problem is that a Bongard Problem can teach its solution to the solver. (See keyword teach.) A large pool of examples can be used for training, as is common in machine learning.

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 247.

CROSSREFS

Adjacent-numbered pages:
BP95 BP96 BP97 BP98 BP99  *  BP101 BP102 BP103 BP104 BP105

KEYWORD

easy, nice, teach, arbitrary, anticomputer, culture, finished, bongard

CONCEPT specific_shape (info | search),
specificity (info | search)

AUTHOR

Mikhail M. Bongard

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