- Counting magic squares and magic cubes
Miklos Bona · 2015
Let us assume that we have to distribute 60 building blocks among three children. Let us say that 20 of the blocks are red, 20 are blue, and 20 are green. To preserve world peace, it is our intention to give 20 blocks to each child. In how many different ways can this be done if blocks of the same color are identical? (Note that the problem is not too interesting if even blocks of the same color are different; indeed, in that case all blocks are different, and the answer is ) · (4020).) This distribution problem is more difficult than the ones we have seen in earlier chapters. In order to understand the problem better, we will represent a possible distribution by a square grid, as shown in Figure 10.1.