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counting and probability junior
Problem
The letters , , , , , and the digits , , , are "cycled" separately as follows and put together in a numbered list: \begin{array}[t]{lccc} & & AJHSME & 1989 \\ & & & \\ 1. & & JHSMEA & 9891 \\ 2. & & HSMEAJ & 8919 \\ 3. & & SMEAJH & 9198 \\ & & ........ & \end{array} What is the number of the line on which will appear for the first time?
(A)
(B)
(C)
(D)
Solution
Every line has as part of it and every line has as part of it. In order for both to be part of line , must be a multiple of and , the least of which is .
Final answer
C