Latin cubes puzzle
Problem:
You have nine red, nine yellow, and nin blue \(1{\times}1{\times}1\) blocks. Can you build a \(3{\times}3{\times}3\) cube, such that exactly color occurs exactly once in each row, column, and file?
Solution:
Yes. Here's one solution:
Going further:
Can you generalize to building an nxnxn cube from \(n\) sets of \(n^2\) \(1{\times}1{\times}1\) cubes?
This problem goes much deeper, as seen here.