24 votes
Accepted

Mishustin's circle problem

Here's my go (click to embiggen) Steps: Connect A to P and pick an arbitrary point Q between them, near-ish to P. Then, draw lines as shown, constructing the points in alphabetical order, which ...
Bass's user avatar
  • 76k
24 votes

Mishustin's circle problem

daw's user avatar
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19 votes
Accepted

Rearrange words to make a sentence

A confusing string of negatives. To put it another way,
codewarrior0's user avatar
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15 votes

Rearrange words to make a sentence

Another take: This is true since
EphraimRuttenberg's user avatar
10 votes

A Prime Ant's Excursion in the Cartesian Plane

melmackian's user avatar
8 votes
Accepted

A Prime Ant's Excursion in the Cartesian Plane

Answer (b) Edit: I was beginning to think that there are only prime solutions, but
Weather Vane's user avatar
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8 votes

A Prime Ant's Excursion in the Cartesian Plane

Here's a (messy) picture proof of optimality for @melmackian's solution: Legend: Red lines: first 3 moves (2,3,5 units) Small black circles with coordinates: some lattice points at a too small prime ...
Bass's user avatar
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8 votes

Rearrange words to make a sentence

Yet another solution: In other words:
Misha Lavrov's user avatar
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7 votes
Accepted

A Sierpiński Carpet ratio

A proof almost without words:
AxiomaticSystem's user avatar
5 votes

A Sierpiński Carpet ratio

This is the result: Here's my own reasoning:
Francesco Sollazzi's user avatar
4 votes
Accepted

Nimber Mnemonics

Multiplication of nimbers between $1$ and $15$ (or between $0$ and $2^{2^n}-1$ for any $n$) has a primitive root: a number whose powers generate all the nimbers we want. (In fact, I believe that $2^{2^...
Misha Lavrov's user avatar
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3 votes
Accepted

Nimber mnemonic combinatorial puzzle

There are 384 solutions. Here's one: I used integer linear programming as follows. Let $$P=\{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o\}$$ be the set of positions, where position $o$ must take ...
RobPratt's user avatar
  • 12k
2 votes

A Sierpiński Carpet ratio

Here is a much simpler way of getting the same answer:
Orntt's user avatar
  • 281
2 votes

Mishustin's circle problem

Note: This is not a valid answer, given the poster's clarification on what the straightedge is capable of. I'm leaving it up because I think it's interesting. I found a way to solve this, based on ...
isaacg's user avatar
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2 votes

A Prime Ant's Excursion in the Cartesian Plane

The ant can return home in I'm not sure if points on the axes count as "in the first quadrant", but I think it's reasonable to permit them, as we require the origin to be the start/end ...
Nuclear Hoagie's user avatar
2 votes

Dissecting a square

A near miss for $D=5$ and $N=7$, with $12$ polyominoes and largest area $8$ instead of $\le 7$: The underlying $5$-regular connected planar graph is the icosahedral graph.
RobPratt's user avatar
  • 12k

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