All Questions

Let $G$ be a finite group with $n = |G|$ elements. By Cayley's theorem for finite groups, we have an injective homomorphism of groups: $$ \pi : G \rightarrow S_n, \quad g \mapsto \pi(g) $$ where ...

I noticed that the new terminal at LaGuardia Airport (in New York) has an intriguing design for the tiles on at least one of their floor areas. It bears a superficial resemblance to aperiodic tilings ...

I got from my children as a gift a puzzle consisting of 25 y-shaped 5-polyominoes that form a $5 \times 5 \times 5$-cube (see picture). I'm wondering for which $n$ does a y-formed $n$-polyomino tile a ...

Recently, the German science journal Spektrum put online a riddle about squares being tiled to a rectangle: The task was to determine the area of the rectangle tiled with $8$ squares, of which the ...

Context: I have a tiling program that uses a directed breadth first search algorithm. It is 'directed' by what I call 'pair scoring'. There are $N$ polyforms (pieces) used in the tiling. I have an $N\...

There's a solution for dividing a square into unique rectangles with the same area which is the blanche dissection. There's also a solution for dividing a square into unique rectangles with the same ...