# Tagged Questions

300 views

### Covering a chess board with $2$ missing places with $31$ dominoes

I am reading a book that is intended to a wide audience (and not just mathematicians etc'), the book is, of course, about mathematics (Its still not clear about what exactly, I am only in page $2$). ...
438 views

### Dissection puzzle for area 49 to area 50

49 and 50 are close, as are 288 and 289. That allows a grid illusion. If cut out of wood, perhaps with coloring on the border as an "assistance", the pieces could be dumped out of the tray, flipping ...
132 views

### Tiling an $n\times n$ Grid

Given an $n\times n$ grid, and $2\times 2$ checkered tiles (white in the upper left and bottom right corners, and black in the upper right and bottom left corners), what is the smallest number of ...
261 views

### Prove or disprove a chessboard with diagonal corners removed, cannot be tiled with L shape pieces or size 2

I think this is impossible, but I don't know how to prove an integer solution doesn't exist for a given equation. Here's my approach: First, observations: The removed tile will be of the same color. ...
415 views

### Hexagon into 12 identical hexagons

Puzzle: Divide a regular hexagon into 12 identical non-convex hexagons. I found this at Jaap Scherphuis' Tiling Applet, and it looks new to me. Are there any solutions other than the one answer ...
293 views

### Tiling pythagorean triples with minimal polyominoes

Given a Pythagorean triple $(a,b,c)$ satisfying $a^2+b^2=c^2$, how to calculate the least number of polyominoes of total squares $c^2$, needed, such that both the square $c^2$ can be build by piecing ...
142 views

### Optimal polyomino induced coloring

Which polyominos (with orientation) of $n$ squares, requires the least number of different colors, $c(n)$, such that if this polyomino is placed anywhere on an optimally colored infinite square grid ...
346 views

### Decomposing a circle into similar pieces

Is it possible to decompose a circle into finitely many similar disjoint pieces, one of which contains the circle's center in its interior?
242 views

### fill the board with dominos

Imagine a 8x8 cell board, but missing two cell at the opposite corners, a domino take up exactly two cell, how to fill the board with dominoes so that none overlap or hang off the edge?
### What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into?
What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into? The image below is a flawed example, from http://www.mathpuzzle.com/flawed456075.gif ...