Search: keyword:hard
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| BP112 |
| X-coordinates of dots are equidistant vs. y-coordinates of dots are equidistant. |
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| BP162 |
| Every other side, if extended, passes through one point vs. not so. |
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| BP344 |
| Shape can tile itself vs. shape cannot tile itself. |
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COMMENTS
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Left examples are sometimes called "rep-tiles."
The tiles all must be the same size. More specifically, all left examples can tile themselves only using scaled down and rotated versions of themselves with all tiles the same size. Right examples cannot tile themselves using scaled down rotated versions of themselves or even reflected versions of themselves with all tiles the same size.
Without the puzzle piece-like shape EX4120 on the right side the current examples also allow the solution "shape can tile with itself so as to create a parallelogram vs. shape cannot tile with itself so as to create a parallelogram." |
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CROSSREFS
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See BP532 for a version with fractals.
Adjacent-numbered pages:
BP339 BP340 BP341 BP342 BP343 * BP345 BP346 BP347 BP348 BP349
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EXAMPLE
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Go to https://oebp.org/files/yet.png for an illustration of how some left-sorted shapes tile themselves. |
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KEYWORD
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hard, nice, precise, notso, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, traditional
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CONCEPT
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recursion (info | search),
self-reference (info | search),
tiling (info | search),
imagined_shape (info | search),
imagined_entity (info | search)
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WORLD
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shape [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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| BP383 |
| When the shape is removed from the dots, the dots give enough information to place the shape back where it was vs. not so. |
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| BP394 |
| For each colored square only, there exists a path starting on it that covers each square of the figure exactly once vs. there is no path that starts on a colored square and covers each square of the figure exactly once. |
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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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| BP801 |
| Number pointed to on number line is "important" mathematical constant vs. not so. |
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