smc

Question

Walking down Jane Street, Ralph passed four houses in a row, each painted a different color. He passed the orange house before the red house, and he passed the blue house before the yellow house. The blue house was not next to the yellow house. How many orderings of the colored houses are possible?

Accepted Answer

Let's use casework on the yellow house. The yellow house (Y) is either the 3^rd house or the last house. Case 1: Y is the 3^rd house. The only possible arrangement is B-O-Y-R Case 2: Y is the last house. There are two possible arrangements: B-O-R-Y O-B-R-Y The answer is 1+2=3