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BP386 Lower shape can be used as a tile to build the upper one vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP381 BP382 BP383 BP384 BP385  *  BP387 BP388 BP389 BP390 BP391

KEYWORD

nice, precise, allsorted, left-narrow, perfect, pixelperfect, orderedpair, traditional, preciseworld, left-listable, right-listable

CONCEPT tiling (info | search)

AUTHOR

Jago Collins

BP394 For each colored square only, there exists a path starting on it that covers each square of the figure exactly once vs. there is no path that starts on a colored square and covers each square of the figure exactly once.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP389 BP390 BP391 BP392 BP393  *  BP395 BP396 BP397 BP398 BP399

KEYWORD

hard, nice, solved, traditional, dithering, left-listable, right-listable

CONCEPT existence (info | search),
path (info | search),
imagined_line_or_curve (info | search),
imagined_entity (info | search)

AUTHOR

Jago Collins

BP904 Rows show all possible ways a certain number of dots can be divided between a certain number of bins vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

The rows in the panels on the right hand side show all the ways you can divide a certain number of dots between a certain number of bins, ignoring which bins they are placed in.

CROSSREFS

Adjacent-numbered pages:
BP899 BP900 BP901 BP902 BP903  *  BP905 BP906 BP907 BP908 BP909

KEYWORD

solved, left-null, grid, left-listable, right-listable

CONCEPT permutation (info | search)

AUTHOR

Molly C Klenzak

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

BP926 Numbers of dots in ascending order from left to right vs. numbers of dots neither in ascending nor descending order from left to right.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP921 BP922 BP923 BP924 BP925  *  BP927 BP928 BP929 BP930 BP931

KEYWORD

nice, math, sequence, traditional, left-listable, right-listable

CONCEPT number (info | search),
dot (info | search)

WORLD

dot_clusters_sequence_horizontal [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP931 Some number labels its own position in the sequence from left to right vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Right examples are called "derangements".

CROSSREFS

Adjacent-numbered pages:
BP926 BP927 BP928 BP929 BP930  *  BP932 BP933 BP934 BP935 BP936

KEYWORD

handed, leftright, sequence, traditional, left-listable, right-listable

CONCEPT number (info | search),
dot (info | search),
self-reference (info | search)

WORLD

dot_clusters_sequence_horizontal [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP956 Nested pairs of brackets vs. other arrangement of brackets (some open brackets are not closed or there are extra closing brackets).
(edit; present; nest [left/right]; search; history)
COMMENTS

Examples on the left are also known as "Dyck words".

REFERENCE

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

CROSSREFS

Adjacent-numbered pages:
BP951 BP952 BP953 BP954 BP955  *  BP957 BP958 BP959 BP960 BP961

KEYWORD

easy, nice, precise, allsorted, unwordable, notso, sequence, traditional, inductivedefinition, preciseworld, left-listable, right-listable

CONCEPT recursion (info | search)

AUTHOR

Aaron David Fairbanks

BP997 There exists a loop that passes through every white square once without passing through the black square vs. there exists no such loop.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP992 BP993 BP994 BP995 BP996  *  BP998 BP999 BP1000 BP1001 BP1002

KEYWORD

precise, allsorted, grid, preciseworld, left-listable, right-listable

CONCEPT path (info | search)

AUTHOR

James Tanton

BP1057 Filled subsection divides the grid vs. not so
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1052 BP1053 BP1054 BP1055 BP1056  *  BP1058 BP1059 BP1060 BP1061 BP1062

KEYWORD

math, grid, left-listable, right-listable

CONCEPT division (info | search),
tiling (info | search)

WORLD

zoom in left

AUTHOR

Jago Collins

BP1072 Filled subsection is largest square that divides the grid vs. not so
(edit; present; nest [left/right]; search; history)
REFERENCE

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

CROSSREFS

Any example in this BP is a left example of BP1057.

Adjacent-numbered pages:
BP1067 BP1068 BP1069 BP1070 BP1071  *  BP1073 BP1074 BP1075 BP1076 BP1077

KEYWORD

grid, left-listable, right-listable

CONCEPT division (info | search)

WORLD

[smaller | same | bigger]

AUTHOR

Jago Collins

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