Search: keyword:perfect
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BP523 |
| Same amount of black in any vertical slice vs. varying amounts of black in vertical slices. |
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BP529 |
| Fractal tiles itself with smaller non-rotated (nor reflected) copies of itself vs. fractal requires turning to tile itself. |
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BP530 |
| Fractal tiles itself with uniformly scaled-down copies of itself vs. fractal tiles itself with stretched copies of itself. |
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BP531 |
| Fractal is tiled by three smaller copies of itself vs. fractal is tiled by five smaller copies of itself. |
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BP532 |
| Self-tiling fractal using one size of tile vs. does not tile itself with a single size of itself. |
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BP533 |
| Contains smaller copy of itself vs. doesn't. |
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BP551 |
| Unstable balance vs. not |
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BP557 |
| Equal horizontal length vs. not |
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BP559 |
| Cross section of a cube vs. not cross section of a cube |
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COMMENTS
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All examples in this Problem are solid black shapes.
This problem is absurdly hard. It makes a good extreme example. - Aaron David Fairbanks, Nov 23 2020 |
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CROSSREFS
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Adjacent-numbered pages:
BP554 BP555 BP556 BP557 BP558  *  BP560 BP561 BP562 BP563 BP564
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KEYWORD
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hard, nice, precise, allsorted, notso, stretch, challenge, left-narrow, perfect
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CONCEPT
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cube (info | search), cross_section (info | search)
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WORLD
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fill_shape [smaller | same | bigger]
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AUTHOR
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Leo Crabbe
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BP564 |
| Discrete points intersecting boundary of convex hull vs. connected segment intersecting boundary of convex hull |
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COMMENTS
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If a "string" is wound tightly around the shape, does one of its segments lie directly on the shape?
All examples in this Problem are connected line segments or curves.
We are taking lines here to be infinitely thin, so that if the boundary of the convex hull intersects the endpoint of a line exactly it is understood that they meet at 1 point. |
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CROSSREFS
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Adjacent-numbered pages:
BP559 BP560 BP561 BP562 BP563  *  BP565 BP566 BP567 BP568 BP569
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EXAMPLE
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Imagine wrapping a string around the pointed star. This string would take the shape of the boundary of the star's convex hull (a regular pentagon), and would only touch the star at the end of each of its 5 individual tips, therefore the star belongs on the left. |
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KEYWORD
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hard, nice, allsorted, solved, perfect
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AUTHOR
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Leo Crabbe
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