I'm having some trouble with a combinatorics problem and I was thinking maybe somebody could give me a little help. I've been thinking about it the entire day and I can't get my head around it. It goes like this.
You have 12 pencils of different colors. How many ways are there to color 2*n (n>2) squares (as in 2 rows, n columns) such that no 2 adjacent squares are painted the same color.
Sorry if my wording is a little bit confusing I translated the problem from spanish. I'll attach an image for better understanding.
I can't do it in any way. I've done this before with n=2 (a square made of 4 smaller squares) and it's a matter of separating into 2 cases, but here I have infinite? cases. It's really confusing. If someone could give me a clue it'd of great help. Thanks!