Problem #8

You are to color each of the squares of an m×n board black or white so that the four corner squares of any rectangle formed by the intersection of a adjacent rows and b adjacent columns (a, b > 1) are not all the same color. An example of such a coloring is shown below for a 3×4 board.

• For a fixed m, what is the largest n for which there is such a coloring of an m×n board?

• Suppose that you use k colors (instead of two) and still require the corner squares of any rectangle not to all be the same color. Now what are the largest possible board sizes?

Back to the Archives

---

Back to the Math Department Homepage.

---