All Questions
Tagged with checkerboard tiling
11
questions
11
votes
1
answer
414
views
A chessboard tiling with corners removed in 3D
A famous problem asks whether an 8x8 chessboard with two opposite corners deleted can be tiled with dominoes, where a domino is a rectangle congruent to two adjacent squares of the board.
Now, let C ...
- 12.3k
9
votes
2
answers
667
views
Covering a chessboard with L-tetrominoes
We all know the classic puzzle of trying to tile a mutilated chessboard with $2\times1$ dominoes. Let's imagine that, instead of dominoes, we have $n^2$ L-shaped tetrominoes and we want to tile a $2n\...
- 117k
10
votes
1
answer
180
views
Combinatorial Agriculture, part 2
Your 64 acre square farm has been doing well and you decide to expand with an orchard. The orchard is also in the form of an 8-by-8 square of subplots, each of which can hold one tree. You have 3 each ...
- 33.7k
8
votes
1
answer
717
views
Jepetto's punctured chessboard [duplicate]
Jepetto the toymaker was thinking about a new toy to add to his tiling product line. His new design involved a punctured chessboard: an ordinary $8 \times 8$ chessboard, except with a single square ...
- 2,567
22
votes
4
answers
4k
views
Mutilated chessboard
Remove the square in the top-left corner of a $2015 \times2015$ chessboard.
Can the remaining mutilated chessboard be tiled with $1\times4$ and $4\times1$ rectangles?
- 2,366
8
votes
4
answers
378
views
Tiling an Odd Polygon with Dominoes
There is a polygon whose edge lengths are all odd integers. Prove that this polygon's interior cannot be tiled by dominoes whose dimensions are $1\times 2$.
An example of such a polygon is a "...
- 32.5k
11
votes
2
answers
380
views
Combinatorial Agriculture
You have just acquired a $64$ acre farm, in the shape of a square, and divided into an eight by eight array of one acre subplots. You have $21$ crops to plant. Each crop requires its own $3$ acre plot ...
- 32.5k
12
votes
3
answers
8k
views
Tiling a Chessboard with tetrominos
Is it possible to tile a $10\times10$ chessboard with (non-overlapping) T-tetrominos?
If so, how? If not, prove it's impossible.
Bonus: Which Tetris pieces can used to tile a 10$\times$10 board, ...
- 32.5k
8
votes
2
answers
750
views
Dominoes on a chessboard
Mary has a box with special $2\times1$ dominoes. Each dominoe has two red corners and two blue corners, and these dominoes come in two different types: The first type has the lower left and the upper ...
- 45.7k
-1
votes
1
answer
444
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Dominoes on a Chess Board [duplicate]
Imagine an 8x8 chessboard has two opposite corners taken out, with 62 squares left over. Is it possible to lay 31 dominoes with the size 2x1 so they cover all of the empty, left over, squares?
- 14.5k
16
votes
2
answers
10k
views
Placing 2x1 dominoes on a chessboard with two corners removed
Suppose you have a checkerboard with two opposite corner squares removed, like this:
Is it possible to place 31 dominoes of size 2x1 so as to cover all of these squares?
- 1,239