MathDB
1989 AJHSME Problem 22

Source:

June 25, 2011
number theoryleast common multiple

Problem Statement

The letters A\text{A}, J\text{J}, H\text{H}, S\text{S}, M\text{M}, E\text{E} and the digits 11, 99, 88, 99 are "cycled" separately as follows and put together in a numbered list: \begin{tabular}[t]{lccc} & & AJHSME & 1989 \\ & & & \\ 1. & & JHSMEA & 9891 \\ 2. & & HSMEAJ & 8919 \\ 3. & & SMEAJH & 9198 \\ & & ........ & \end{tabular}
What is the number of the line on which AJHSME 1989\text{AJHSME 1989} will appear for the first time?
(A) 6(B) 10(C) 12(D) 18(E) 24\text{(A)}\ 6 \qquad \text{(B)}\ 10 \qquad \text{(C)}\ 12 \qquad \text{(D)}\ 18 \qquad \text{(E)}\ 24
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