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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

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

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

BP1282 If two players take turns moving moving the black circles with the intention of capturing their opponent's piece, one can always "checkmate" the other vs. the game results in a draw if the players play optimally.
(edit; present; nest [left/right]; search; history)
COMMENTS

Players can only move their piece to a node connected to their current position. A win is secured by moving to a node your opponent is occupying.


Which player that can force a win in left-sorted examples can change depending on who moves first.

CROSSREFS

See BP1284 for an animated Problem about the same game.

Adjacent-numbered pages:
BP1277 BP1278 BP1279 BP1280 BP1281  *  BP1283 BP1284 BP1285 BP1286 BP1287

KEYWORD

allsorted, unwordable, notso, teach

CONCEPT capture_game (info | search)

AUTHOR

Leo Crabbe

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