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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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BP389 |
| Loops are entangled (in 3-D) vs. loops can be separated (in 3-D). |
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BP390 |
| Each graph vertex is uniquely defined by its connections (the graph does not admit nontrivial automorphisms) vs. the graph admits nontrivial automorphisms. |
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BP527 |
| Each black filled circle belongs to exactly one large circle outline vs. not so. |
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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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BP560 |
| There exists a closed trail that hits each edge exactly once vs. not so. |
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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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BP569 |
| Triangular number of dots vs. non-triangular number of dots |
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COMMENTS
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All examples in this Problem are groups of black dots.
The nth triangular number is the sum over the natural numbers from 1 to n, where n > 0. Note: 0 is the 0th triangular number. The first few triangular numbers are 0, 1, 3 (= 1+2) and 6 (= 1+2+3) |
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CROSSREFS
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Adjacent-numbered pages:
BP564 BP565 BP566 BP567 BP568  *  BP570 BP571 BP572 BP573 BP574
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KEYWORD
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nice, precise, allsorted, notso, number, math, left-narrow, left-null, help, preciseworld
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WORLD
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dots [smaller | same | bigger]
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AUTHOR
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Leo Crabbe
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