"The number of common letters between my two colors is one less than the number of A's common letters and one more than the number of C's common letters."
Find the colors each person received. Is there more than one answer?
(For this discussion, dual letters are only counted once. For example, yellow and purple have only two common letters: e and l.)
Below is a matrix showing the number of common letters between each pair of colors: *blue 1 *green 1 4 *orange 3 2 2 *purple 1 2 2 2 *red 2 1 2 2 1 *yellow Here the color attached to the * applies to each entry to the left of the * and directly below it. For example, the 3 in the left column is under *blue and left of *purple, so that entry refers the the three common letters between blue and purple. Since there are only 4 distinct values in the matrix, the number of common letters for A B C is either 4 3 2 or 3 2 1. Simple examination discloses one solution: [Larry Baum's analysis insered here - KD] So either A=4 (orange/green) or 3 (blue/purple) If A=4, then B=3 (blue/purple), which leaves (red/yellow)=1 for C, but we would need C=2. So A=3 (blue/purple). Then C=1 must be either red/yellow or green/yellow leaving B= orange/green(4) or orange/red(2). Only the latter works. A 3 purple/blue B 2 orange/red C 1 yellow/green