All Questions
5
questions
10
votes
1
answer
180
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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
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
-1
votes
1
answer
444
views
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?
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