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BP1271 Positive correlation vs. negative correlation.
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(edit; present; nest [left/right]; search; history)
COMMENTS

All examples in this Bongard Problem are scatter plots. Each dot represents a data point.

"Positive correlation" means that when the X value increases, the Y value tends to increase as well (in the long run), while "negative correlation" means that when the X value increases, the Y value tends to decrease.

CROSSREFS

Adjacent-numbered pages:
BP1266 BP1267 BP1268 BP1269 BP1270  *  BP1272 BP1273 BP1274 BP1275 BP1276

EXAMPLE

Example TM4854 does not fit on either side because when the X value increases, the Y value stays the same.

Example TM4855 does not fit on either side because there is no correlation.

KEYWORD

fuzzy, minimal, unwordable, teach, spectrum, dual, handed, leftright, updown, rotate, stable, hardsort, left-narrow, right-narrow

AUTHOR

Ben

BP1272 Square minus circle vs. circle minus square.
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(edit; present; nest [left/right]; search; history)
COMMENTS

All examples in this Bongard Problem are solid black shapes.

CROSSREFS

BP345 is "Intersection of circle and square vs. union of circle and square."

Adjacent-numbered pages:
BP1267 BP1268 BP1269 BP1270 BP1271  *  BP1273 BP1274 BP1275 BP1276 BP1277

EXAMPLE

EX1 is ambiguous because it might be a small circle minus a large square, or a small square minus a large circle.

KEYWORD

easy, nice, precise, dual

CONCEPT subtraction (info | search),
overlap (info | search)

AUTHOR

Ben

BP1273 Sequence contains each possible way its distinct elements can be arranged as a subsequence vs. not so.
(edit; present; nest [left/right]; search; history)
REFERENCE

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

CROSSREFS

Adjacent-numbered pages:
BP1268 BP1269 BP1270 BP1271 BP1272  *  BP1274 BP1275 BP1276 BP1277 BP1278

EXAMPLE

There are 6 ways of arranging the letters A, B and C: ABC, ACB, BAC, BCA, CAB, and CBA. The string "ABCABACBA" contains each of these as a substring, and would therefore be sorted left.

KEYWORD

precise, allsorted, notso, sequence, traditional, miniworlds

CONCEPT sequence (info | search),
overlap (info | search)

WORLD

[smaller | same | bigger]

AUTHOR

Leo Crabbe

BP1274 Reversing the sequence permutes the objects vs. not.
(edit; present; nest [left/right]; search; history)
COMMENTS

Equivalently, some permutation of the objects reverses the sequence vs. not.


Palindromes fit left. Strings of distinct objects repeated any number of times fit left.

CROSSREFS

Adjacent-numbered pages:
BP1269 BP1270 BP1271 BP1272 BP1273  *  BP1275 BP1276 BP1277 BP1278 BP1279

KEYWORD

nice, precise, allsorted, notso, sequence, miniworlds

WORLD

[smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1275 There is a way of grouping elements into (more than one) equal-sized blocks such that no block appears twice vs. there exists no such grouping.
(edit; present; nest [left/right]; search; history)
COMMENTS

Sequences with a prime number of elements are sorted left when all their elements are unique, and sorted right otherwise.

CROSSREFS

Adjacent-numbered pages:
BP1270 BP1271 BP1272 BP1273 BP1274  *  BP1276 BP1277 BP1278 BP1279 BP1280

EXAMPLE

The sequence ABBABB would be sorted left, as it could be grouped into (AB)(BA)(BB), where each block is unique.

KEYWORD

precise, unwordable, notso, sequence, miniworlds

CONCEPT element_grouping (info | search)

AUTHOR

Leo Crabbe

BP1276 Ways of representing the sequence "ABABCBACCBAC" by grouping its elements into equal-sized blocks and relabelling them (identical blocks are represented by the same element) vs. representations of different sequences.
(edit; present; nest [left/right]; search; history)
COMMENTS

The solver isn't expected to word their solution as it is put above, but to notice that the sequences on the left all "agree" with each other under the aforementioned grouping rule. The 12-element sequence in EX10249 can be "squashed down" into the 6-element sequence in EX10251, which in turn can be "squashed down" into the 3-element sequence in EX10252.

CROSSREFS

Compare to BP121

Adjacent-numbered pages:
BP1271 BP1272 BP1273 BP1274 BP1275  *  BP1277 BP1278 BP1279 BP1280 BP1281

KEYWORD

unwordable, notso, arbitrary, sequence

CONCEPT element_grouping (info | search)

AUTHOR

Leo Crabbe

BP1278 There is a way of dividing the grid into (more than one) equal-sized blocks such that no block appears more than once vs. there exists no such way of dividing the grid.
(edit; present; nest [left/right]; search; history)
CROSSREFS

2D version of BP1275.

Adjacent-numbered pages:
BP1273 BP1274 BP1275 BP1276 BP1277  *  BP1279 BP1280 BP1281 BP1282 BP1283

KEYWORD

precise, traditional, grid

AUTHOR

Leo Crabbe

BP1279 Circled points are all possible vertices a square with a particular side length can take, provided that each of its corners lie on a grid point vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Rotation of the square is allowed.

CROSSREFS

See BP1280 for version with hexagons on a hexagonal grid.

Adjacent-numbered pages:
BP1274 BP1275 BP1276 BP1277 BP1278  *  BP1280 BP1281 BP1282 BP1283 BP1284

KEYWORD

hard, precise, allsorted, unwordable, hardsort, left-finite, right-finite, left-full, fixedgrid, preciseworld

CONCEPT square (info | search)

AUTHOR

Leo Crabbe

BP1280 Circled points are all possible vertices a regular hexagon with a particular side length can take, provided that each of its corners lie on a grid point vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

See BP1279 for version with squares on a square grid.

Adjacent-numbered pages:
BP1275 BP1276 BP1277 BP1278 BP1279  *  BP1281 BP1282 BP1283 BP1284 BP1285

KEYWORD

hard, precise, allsorted, unwordable, hardsort, left-finite, right-finite, preciseworld

AUTHOR

Leo Crabbe

BP1281 Circled points are all possible vertices an equilateral triangle with a particular side length can take, provided that each of its corners lie on a grid point vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1276 BP1277 BP1278 BP1279 BP1280  *  BP1282 BP1283 BP1284 BP1285 BP1286

KEYWORD

unwordable, left-finite, right-finite, preciseworld

CONCEPT triangle (info | search)

AUTHOR

Leo Crabbe

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