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BP1159 Bongard Problems where examples are only sorted left if nothing indicates that they would be sorted right vs. vice-versa.
BP250
BP333
BP525
BP823
BP1230
BP1183
(edit; present; nest [left/right]; search; history)
COMMENTS

Left-sorted Bongard Problems have the keyword "left-couldbe" on the OEBP.

Right-sorted Bongard Problems have the keyword "right-couldbe".


In a "couldbe" Bongard Problem, some relevant information is left out by the way objects are displayed. Solutions to "left-couldbe" BPs sound like "Could be a ___ vs. definitely not a ___" (and vice versa for "right-couldbe" BPs.)



To put it in mathematical jargon, there is a "projection" function from objects to pictures, such that objects satisfying property X are mapped to the same picture as objects not satisfying property X. Sorted on the "couldbe" side is the image (under projection) of the collection of objects satisfying property X.


Furthermore, usually X is a relatively narrow criterion, so that most objects do not satisfy it (see keywords left-narrow and right-narrow), and all pictures are in the image (under projection) of the collection of objects not satisfying property X.

REFERENCE

Consider BP525, "Cropped image of a circle vs. not so." None of the left-hand examples are definitely an image of a circle, but they fit left because nothing indicates that they are not an image of a circle. A more pedantic solution to this Bongard Problem would be "There is a way of cropping a circle that gives this image vs. there isn't."

CROSSREFS

See also the keyword seemslike, where neither side can be confirmed.


Either "left-couldbe" or "right-couldbe" implies notso.


Although the descriptions of "left-couldbe" and "right-couldbe" sound similar to left-unknowable and right-unknowable, they are not the same. It is the difference between a clear absence of information and perpetual uncertainty about whether there is more information to be found.


"Left-couldbe" is usually left-narrow and "right-couldbe" usually right-narrow.

Adjacent-numbered pages:
BP1154 BP1155 BP1156 BP1157 BP1158  *  BP1160 BP1161 BP1162 BP1163 BP1164

KEYWORD

dual, meta (see left/right), links, keyword, side, viceversa

AUTHOR

Leo Crabbe

BP1208 More triangles left than right vs. more triangles right than left.
(edit; present; nest [left/right]; search; history)
COMMENTS

The triangles vary in size in order to make the solution clearly about quantity, not "total mass".

CROSSREFS

Adjacent-numbered pages:
BP1203 BP1204 BP1205 BP1206 BP1207  *  BP1209 BP1210 BP1211 BP1212 BP1213

KEYWORD

stub, precise, spectrum, dual, handed, leftright, traditional

CONCEPT number (info | search),
triangle (info | search),
quantity_comparison (info | search)

AUTHOR

Aaron David Fairbanks

BP1213 Axis of symmetry along the NW/SE diagonal vs. axis of symmetry along the NE/SW diagonal
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1208 BP1209 BP1210 BP1211 BP1212  *  BP1214 BP1215 BP1216 BP1217 BP1218

KEYWORD

stub, dual, handed, leftright, updown, rotate, stretch, left-narrow, right-narrow, traditional, both

CONCEPT diagonal (info | search),
symmetry_axis (info | search),
symmetry (info | search)

AUTHOR

Aaron David Fairbanks

BP1214 Left shape is bigger than right shape vs. right shape is bigger than left shape.
(edit; present; nest [left/right]; search; history)
CROSSREFS

BP1217 has the same solution but rotated a quarter-turn counter-clockwise.

Adjacent-numbered pages:
BP1209 BP1210 BP1211 BP1212 BP1213  *  BP1215 BP1216 BP1217 BP1218 BP1219

KEYWORD

stub, dual, handed, leftright, traditional

CONCEPT size (info | search),
quantity_comparison (info | search)

AUTHOR

Aaron David Fairbanks

BP1216 Arrow pointing north-west vs. arrow pointing south-east.
(edit; present; nest [left/right]; search; history)
CROSSREFS

BP1218 is "arrow pointing north-west vs. arrow pointing elsewhere".

Adjacent-numbered pages:
BP1211 BP1212 BP1213 BP1214 BP1215  *  BP1217 BP1218 BP1219 BP1220 BP1221

KEYWORD

stub, precise, dual, handed, leftright, updown, rotate, left-narrow, right-narrow, traditional

CONCEPT diagonal (info | search)

AUTHOR

Aaron David Fairbanks

BP1217 Bottom shape is bigger than top shape vs. top shape is bigger than bottom shape.
(edit; present; nest [left/right]; search; history)
CROSSREFS

BP1214 has the same solution but rotated a quarter-turn clockwise.

Adjacent-numbered pages:
BP1212 BP1213 BP1214 BP1215 BP1216  *  BP1218 BP1219 BP1220 BP1221 BP1222

KEYWORD

stub, dual, handed, updown, traditional

CONCEPT size (info | search),
quantity_comparison (info | search)

AUTHOR

Aaron David Fairbanks

BP1245 When two players alternate coloring regions, either can force connection from top edge to bottom edge vs. either can force connection from left edge to right edge.
(edit; present; nest [left/right]; search; history)
REFERENCE

https://en.wikipedia.org/wiki/Hex_(board_game)

CROSSREFS

Adjacent-numbered pages:
BP1240 BP1241 BP1242 BP1243 BP1244  *  BP1246 BP1247 BP1248 BP1249 BP1250

KEYWORD

hard, precise, convoluted, dual, rotate, boundingbox, hardsort, challenge, proofsrequired, bordercontent

AUTHOR

Aaron David Fairbanks

BP1254 Bongard Problems with solutions of the form "[X] vs. [representation of X]" vs. vice versa.
BP1126
BP1219
BP1253
BP1056
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1249 BP1250 BP1251 BP1252 BP1253  *  BP1255 BP1256 BP1257 BP1258 BP1259

KEYWORD

dual, meta (see left/right), links, viceversa

AUTHOR

Leo Crabbe

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