A rainbow-coloured table

Probability Level 4

A $15\times n$ table (where n is a positive integer) is divided into $1\times 1$ squares. Each square is coloured red, orange, yellow, green, blue, indigo, or violet.

Find the minimum value for $n$ so that for any coloring of the table, so that one can pick three rows and columns with all nine intersections being the same color.

The answer is 6371.

1 solution

Luca Minuel
Apr 23, 2017

Each column has a color that is repeated at least once (pigeonhole) . Rows are 15, so we can choose intersections in ${15 \choose 3}$ ways, mulitiply for $7$ (colors). If we multiply it for 2, we'll get a table wrong, but any additional column makes the last one ok. So $n$ is:

${15 \choose 3}$ $\cdot$ $7 \cdot 2$ $+ 1$ $=$ $\boxed {6371}$

A rainbow-coloured table

The answer is 6371.

1 solution

0 pending reports