2000 CEMC Pascal Problems/Problem 4

Problem

If the following sequence of five arrows repeats itself continuously, what arrow would be in the $48$ th position?

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There are five arrows in the sequence, so the pattern will repeat for every $5$ positions.

This means that we can just find the remainder when dividing $48$ by $5$ . $5 \times 9 = 45$ , but $5 \times 10 = 50$ .

Since $48$ is between these two numbers, the remainder must be $48 - 45 = 3$ .

The third arrow in the pattern is $\boxed {\textbf {(C) }}$ .

~anabel.disher