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BP1192 Short, short, long, short, long vs. not.
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples in this Problem are paths of short and long line segments which do not self-intersect. This could be a useful world to use in an abstract binary sequence BP.

CROSSREFS

Adjacent-numbered pages:
BP1187 BP1188 BP1189 BP1190 BP1191  *  BP1193 BP1194 BP1195 BP1196 BP1197

KEYWORD

nice, notso, arbitrary, traditional

WORLD

[smaller | same | bigger]

AUTHOR

Jago Collins

BP1193 Long, short, short, short vs. short, long, long, short
(edit; present; nest [left/right]; search; history)
COMMENTS

In morse code, the solution to this BP is B vs. P.

CROSSREFS

Adjacent-numbered pages:
BP1188 BP1189 BP1190 BP1191 BP1192  *  BP1194 BP1195 BP1196 BP1197 BP1198

KEYWORD

arbitrary, funny, neither

WORLD

[smaller | same | bigger]

AUTHOR

Jago Collins

BP1197 No sequence is repeated twice in a row vs. some sequence is repeated twice in a row.
(edit; present; nest [left/right]; search; history)
REFERENCE

https://en.wikipedia.org/wiki/Square-free_word

CROSSREFS

Adjacent-numbered pages:
BP1192 BP1193 BP1194 BP1195 BP1196  *  BP1198 BP1199 BP1200 BP1201 BP1202

KEYWORD

precise, allsorted, notso, left-narrow, sequence, traditional, preciseworld, dithering, left-listable

CONCEPT two (info | search)

AUTHOR

Aaron David Fairbanks

BP1199 The only rectangles are the individual regions and the whole vs. there is some other rectangle made of rectangles.
(edit; present; nest [left/right]; search; history)
CROSSREFS

All of the examples fitting left here would fit right in BP1200 except for (1) a single rectangle, (2) two rectangles stacked vertically, or (3) two rectangles side by side horizontally.


All of the examples fitting left in BP1097 (re-styled) would fit right here (besides the two possible arrangements made up of just two rectangles, but those aren't shown there).


See BP1201 for the version with triangles.

Adjacent-numbered pages:
BP1194 BP1195 BP1196 BP1197 BP1198  *  BP1200 BP1201 BP1202 BP1203 BP1204

KEYWORD

precise, traditional, left-listable, right-listable

AUTHOR

Aaron David Fairbanks

BP1200 The whole rectangle can be filled in by successively replacing pairs of adjacent rectangles with one vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Another wording: "can be repeatedly broken along 'fault lines' to yield individual pieces vs not."

REFERENCE

Robert Dawson, A forbidden suborder characterization of binarily composable diagrams in double categories, Theory and Applications of Categories, Vol. 1, No. 7, p. 146-145, 1995.

CROSSREFS

All of the examples fitting left here would fit right in BP1199 except for (1) a single rectangle, (2) two rectangles stacked vertically, or (3) two rectangles side by side horizontally.


All of the examples fitting right in in BP1097 (re-styled) would fit right here (besides a single solid block, but that isn't shown there).

Adjacent-numbered pages:
BP1195 BP1196 BP1197 BP1198 BP1199  *  BP1201 BP1202 BP1203 BP1204 BP1205

KEYWORD

hard, precise, challenge, proofsrequired, inductivedefinition, left-listable, right-listable

AUTHOR

Aaron David Fairbanks

BP1201 The only triangles are the individual regions and the whole vs. there is some other triangle made of triangles.
(edit; present; nest [left/right]; search; history)
CROSSREFS

See BP1199 for the version with rectangles.

Adjacent-numbered pages:
BP1196 BP1197 BP1198 BP1199 BP1200  *  BP1202 BP1203 BP1204 BP1205 BP1206

KEYWORD

precise, traditional, left-listable, right-listable

CONCEPT triangle (info | search)

AUTHOR

Aaron David Fairbanks

BP1202 Color of any region is an equal mix of the colors of the overlapping shapes vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1197 BP1198 BP1199 BP1200 BP1201  *  BP1203 BP1204 BP1205 BP1206 BP1207

KEYWORD

precise, allsorted, notso, color

AUTHOR

Leo Crabbe

BP1206 Vertical axis of symmetry vs. no vertical axis of symmetry.
(edit; present; nest [left/right]; search; history)
COMMENTS

The solution for this Bongard Problem is also a (less specific) solution for BP500, "vertical axis of symmetry vs. no axis of symmetry".

CROSSREFS

BP1207 is the same solution but using the horizontal axis instead of the vertical axis.

BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.

Adjacent-numbered pages:
BP1201 BP1202 BP1203 BP1204 BP1205  *  BP1207 BP1208 BP1209 BP1210 BP1211

KEYWORD

stub, notso, stretch, left-narrow, traditional

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

AUTHOR

Aaron David Fairbanks

BP1207 Horizontal axis of symmetry vs. no horizontal axis of symmetry.
(edit; present; nest [left/right]; search; history)
CROSSREFS

BP1206 is the same solution but using the vertical axis instead of the horizontal axis.

BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.

Adjacent-numbered pages:
BP1202 BP1203 BP1204 BP1205 BP1206  *  BP1208 BP1209 BP1210 BP1211 BP1212

KEYWORD

stub, notso, stretch, left-narrow, traditional

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

AUTHOR

Aaron David Fairbanks

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

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