This problem is from Problem Solving Strategies - Crossing the River with Dogs and Other Mathematical Adventures by Ken Johnson and Ted Herr.
I first let capital letters denote shirts, and lowercase letters denote ties (with one letter representing each to make things easier).
So, B = blue, G = green, W = white, P = blue and green print, and S = red and white striped shirt.
I also made w = white, b = blue, y = yellow, p = green and blue striped tie
Then, I began working out the possible combinations:
For (color) shirt:
Blue (no blue tie, pattern much include blue [as denoted in the problem]): Bw, By, Bp
Green (no green tie, patter much include green): Gw, Gb, Gy, Gp
White: Wb, Wy
Blue and Green Pattern (P): Pb
Red and white stripe (S): Sw
I am wondering if there are any possibilities I missed. As of now, I have worked out there to be 11 combinations, with 6 out of the 11 involving the color blue. Any help would be much appreciated.