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A flagpole is n feet tall. On this pole we display flags of the following types: red flags that are 1 foot tall, blue flags that are 2 feet tall, and green flags that are 2 feet tall. The sum of the heights of the flags is exactly n feet. Prove that there are
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A class of n children sits in a circle. The teacher walks around the outside of the circle and pats every k-th child on the head. Find and prove a necessary and sufficient condition on n and k so that every child receives a pat on the head. |
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ways to display the flags.
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