Search: keyword:left-narrow
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BP1 |
| Empty image vs. non-empty image. |
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COMMENTS
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The first Bongard Problem.
All examples in this Bongard Problem are line drawings (one or more connected figures made up of curved and non-curved lines). |
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REFERENCE
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M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214. |
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CROSSREFS
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Adjacent-numbered pages:
  *  BP2 BP3 BP4 BP5 BP6
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EXAMPLE
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A circle fits on the right because it is not nothing. |
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KEYWORD
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easy, nice, precise, allsorted, unstable, world, left-narrow, left-finite, left-full, left-null, perfect, pixelperfect, finished, traditional, stableworld, deformstable, bongard
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CONCEPT
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empty (info | search), existence (info | search), zero (info | search)
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WORLD
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zoom in left (blank_image) | zoom in right (curves_drawing)
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AUTHOR
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Mikhail M. Bongard
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BP31 |
| One line vs. two lines. |
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REFERENCE
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M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224. |
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CROSSREFS
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Adjacent-numbered pages:
BP26 BP27 BP28 BP29 BP30  *  BP32 BP33 BP34 BP35 BP36
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KEYWORD
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easy, precise, allsorted, left-narrow, right-narrow, pixelperfect, traditional, bongard
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CONCEPT
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distinguishing_crossing_curves (info | search), one (info | search), two (info | search)
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WORLD
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smooth_crosscurves [smaller | same | bigger]
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AUTHOR
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Mikhail M. Bongard
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BP50 |
| Vertical axis of symmetry vs. no axis of symmetry. |
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REFERENCE
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M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230. |
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CROSSREFS
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BP152 is the same solution (with the sides switched), using connected shapes and without black filling.
BP1206 was created to be a slightly different version of this: "vertical axis of symmetry vs. no vertical axis of symmetry." (That less specific solution fits this Bongard Problem as well.)
Adjacent-numbered pages:
BP45 BP46 BP47 BP48 BP49  *  BP51 BP52 BP53 BP54 BP55
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KEYWORD
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nice, stretch, left-narrow, finished, traditional, bongard
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CONCEPT
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symmetry_axis (info | search), symmetry (info | search)
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WORLD
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curves_and_fill_shapes_separate_drawing [smaller | same | bigger]
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AUTHOR
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Mikhail M. Bongard
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BP328 |
| All sides are equal vs. all angles are equal. |
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BP334 |
| Odd number of dots vs. even number of dots. |
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CROSSREFS
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See BP334 for a version of the same idea, but using arbitrary shapes instead of dots.
Adjacent-numbered pages:
BP329 BP330 BP331 BP332 BP333  *  BP335 BP336 BP337 BP338 BP339
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KEYWORD
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precise, allsorted, number, math, left-narrow, right-narrow, right-null, help, traditional, preciseworld
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CONCEPT
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even_odd (info | search)
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WORLD
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dots [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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BP345 |
| Intersection of circle and square vs. union of circle and square. |
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BP356 |
| Object at lower-right fits as n-th item in the top row of objects, where n is the number of dots at lower-left vs. not so. |
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COMMENTS
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All examples have a number of dots in the bottom left corner, an object in the bottom right corner, and a sequence of object at the top. |
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CROSSREFS
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Adjacent-numbered pages:
BP351 BP352 BP353 BP354 BP355  *  BP357 BP358 BP359 BP360 BP361
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KEYWORD
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nice, creativeexamples, left-narrow, structure, traditional, rules, miniworlds
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CONCEPT
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fractal (info | search), iteration (info | search), tracing_line_or_curve (info | search), feature_cluster (info | search), shape_cluster (info | search), cluster (info | search)
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AUTHOR
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Aaron David Fairbanks
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BP373 |
| Intersection (logical conjunction) vs. union (logical disjunction). |
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CROSSREFS
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Adjacent-numbered pages:
BP368 BP369 BP370 BP371 BP372  *  BP374 BP375 BP376 BP377 BP378
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KEYWORD
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abstract, anticomputer, concept, creativeexamples, left-narrow, right-narrow, contributepairs, traditional, miniworlds, dithering
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CONCEPT
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set_intersection (info | search), set_union (info | search)
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AUTHOR
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Aaron David Fairbanks
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BP384 |
| Square number of dots vs. non-square number of dots. |
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COMMENTS
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All examples in this Problem are a collection of dots.
An equivalent solution is "Dots can be arranged into a square lattice whose convex hull is a square vs. not so". - Leo Crabbe, Aug 01 2020 |
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CROSSREFS
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Adjacent-numbered pages:
BP379 BP380 BP381 BP382 BP383  *  BP385 BP386 BP387 BP388 BP389
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EXAMPLE
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A single dot fits because 1 = 1*1.
A pair of dots does not fit because there is no integer x such that 2 = x*x. |
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KEYWORD
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nice, precise, allsorted, number, math, left-narrow, left-null, help, traditional, preciseworld, collection
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CONCEPT
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square_number (info | search)
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WORLD
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dots [smaller | same | bigger]
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AUTHOR
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Jago Collins
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BP386 |
| Lower shape can be used as a tile to build the upper one vs. not so. |
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CROSSREFS
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Adjacent-numbered pages:
BP381 BP382 BP383 BP384 BP385  *  BP387 BP388 BP389 BP390 BP391
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KEYWORD
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nice, precise, allsorted, left-narrow, perfect, pixelperfect, orderedpair, traditional, preciseworld, left-listable, right-listable
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CONCEPT
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tiling (info | search)
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AUTHOR
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Jago Collins
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