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BP559 Cross section of a cube vs. not cross section of a cube
?
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples are solid black shapes.


This problem is absurdly hard. It makes a good extreme example. - Aaron David Fairbanks, Nov 23 2020

CROSSREFS

Adjacent-numbered pages:
BP554 BP555 BP556 BP557 BP558  *  BP560 BP561 BP562 BP563 BP564

KEYWORD

hard, precise, allsorted, notso, stretch, challenge, left-narrow, perfect

CONCEPT cube (info | search),
cross_section (info | search)

WORLD

fill_shape [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP569 Triangular number of dots vs. non-triangular number of dots
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples in this Problem are groups of black dots.


The nth triangular number is the sum over the natural numbers from 1 to n, where n > 0. Note: 0 is the 0th triangular number. The first few triangular numbers are 0, 1, 3 (= 1+2) and 6 (= 1+2+3)

CROSSREFS

Adjacent-numbered pages:
BP564 BP565 BP566 BP567 BP568  *  BP570 BP571 BP572 BP573 BP574

KEYWORD

nice, precise, allsorted, notso, number, math, left-narrow, left-null, help, preciseworld

WORLD

dots [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP850 Shape can be maneuvered around the corner vs. not so.
(edit; present; nest [left/right]; search; history)
REFERENCE

https://en.wikipedia.org/wiki/Moving_sofa_problem

CROSSREFS

Adjacent-numbered pages:
BP845 BP846 BP847 BP848 BP849  *  BP851 BP852 BP853 BP854 BP855

KEYWORD

nice, precise, physics, creativeexamples, proofsrequired, left-narrow, right-narrow, dithering

CONCEPT rotation_required (info | search),
imagined_motion (info | search),
physically_fitting (info | search)

AUTHOR

Leo Crabbe

BP856 Compound shape would hit the dot if rotated vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP851 BP852 BP853 BP854 BP855  *  BP857 BP858 BP859 BP860 BP861

KEYWORD

nice, precise, allsorted, left-narrow, preciseworld

CONCEPT imagined_motion (info | search),
collision (info | search)

AUTHOR

Leo Crabbe

BP902 This Bongard Problem vs. anything else.
BP902
BP1

becious

(edit; present; nest [left/right]; search; history)
COMMENTS

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.

CROSSREFS

See BP953, BP959.

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

KEYWORD

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

CONCEPT self-reference (info | search),
specificity (info | search)

WORLD

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

AUTHOR

Leo Crabbe

BP922 One row is rearranged to make the other by swapping an odd number of object pairs vs. one row is rearranged to make the other by swapping an even number of object pairs.
(edit; present; nest [left/right]; search; history)
COMMENTS

The mathematical terms for these operations are even and odd permutations.

CROSSREFS

Adjacent-numbered pages:
BP917 BP918 BP919 BP920 BP921  *  BP923 BP924 BP925 BP926 BP927

KEYWORD

precise, allsorted, math, left-narrow, right-narrow, unorderedpair, preciseworld, left-listable

CONCEPT even_odd (info | search),
permutation (info | search)

AUTHOR

Leo Crabbe

BP932 Every vertex is connected to every other vs. vertices are connected in a cycle (no other connections).
?
?
(edit; present; nest [left/right]; search; history)
COMMENTS

Complete graphs with zero, one, two, or three vertices would be ambiguously categorized (fit in overlap of both sides).


Left examples are called "fully connected graphs." Right examples are called "cycle graphs."

CROSSREFS

Adjacent-numbered pages:
BP927 BP928 BP929 BP930 BP931  *  BP933 BP934 BP935 BP936 BP937

KEYWORD

precise, left-narrow, right-narrow, both, preciseworld

CONCEPT graph (info | search),
distinguishing_crossing_curves (info | search),
all (info | search),
loop (info | search)

WORLD

connected_graph [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP935 Shapes have equal area vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP930 BP931 BP932 BP933 BP934  *  BP936 BP937 BP938 BP939 BP940

KEYWORD

nice, precise, allsorted, unstable, left-narrow, perfect, pixelperfect, unorderedpair

CONCEPT area (info | search)

WORLD

2_fill_shapes [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP937 Shapes have equal perimeter vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP932 BP933 BP934 BP935 BP936  *  BP938 BP939 BP940 BP941 BP942

KEYWORD

precise, allsorted, unstable, left-narrow, perfect, unorderedpair

CONCEPT perimeter (info | search)

WORLD

2_fill_shapes [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP988 Number of dots is a power of 2 vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Numbers of dots on the left can be obtained by repeatedly doubling 1 dot.

Numbers of dots on the left are the number of corners of a cube in some dimension.

CROSSREFS

Adjacent-numbered pages:
BP983 BP984 BP985 BP986 BP987  *  BP989 BP990 BP991 BP992 BP993

KEYWORD

stub, precise, allsorted, number, left-narrow, right-null, help, preciseworld

WORLD

dots [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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