Problem:
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?
Answer Choices:
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Solution:
If Ralph passed the orange house first, then because the blue and yellow houses are not neighbors, the house color ordering must be orange, blue, red, yellow. If Ralph passed the blue house first, then there are possible placements for the yellow house, and each choice determines the placement of the orange and red houses. These house color orderings are blue, orange, yellow, red, and blue, orange, red, yellow. There are possible orderings for the colored houses.
The problems on this page are the property of the MAA's American Mathematics Competitions