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 ...
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
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 ...
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^...
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 ...
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
...
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 ...
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.
Only top scored, non community-wiki answers of a minimum length are eligible
Related Tags
geometry × 1100mathematics × 565
dissection × 104
optimization × 98
visual × 92
logical-deduction × 83
combinatorics × 69
three-dimensional × 69
tiling × 66
polyomino × 42
strategy × 39
calculation-puzzle × 33
no-computers × 33
pattern × 31
construction × 29
paper-folding × 28
packing × 28
triangle × 26
graph-theory × 23
computer-puzzle × 22
enigmatic-puzzle × 21
lateral-thinking × 19
story × 17
word-problem × 17
matches × 16