Daniel Berend

In this paper we consider a question raised in [4] regarding Paint-by-Numbers puzzles. Paint-by-Numbers is a classic logic puzzle in which the squares of a p × n grid are to be colored black or white, according to hints, consisting of the length of the blocks of consecutive black squares in each row and column. Mullen [4] studied the asymptotic probability that a random hint sequence of a row will determine uniquely the color of at least some of the squares in a row, and was able to give lower and upper bounds on this probability. In this paper we tighten his bounds.