Several identical paper squares of $n$ different colors are lying on a rectangular table, with sides of the squares parallel to the sides of the table. Among any $n$ squares of pairwise distinct colors, it is possible to find $2$ which can be pinned to the table using one pin. Prove that all the squares of a certain color can be pinned to the table using $2n-2$ pins.
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
Let's induct on the number of colors, $n$
When $n$ is 2 (as @goodarz suggests) we do the following:
Now assuming the statement holds for $n-1$: