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 ...
- 76k
24
votes
19
votes
Accepted
15
votes
10
votes
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
- 13.7k
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 ...
- 76k
8
votes
7
votes
Accepted
5
votes
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^...
- 1,779
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 ...
- 12k
2
votes
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
...
- 5,461
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 ...
- 4,499
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.
- 12k
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