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1968 AMC 12 #33 - Base 7 and Base 9

Source:

January 1, 2012
number theorygreatest common divisorAMC

Problem Statement

A number NN has three digits when expressed in base 77. When NN is expressed in base 99 the digits are reversed. Then the middle digit is:
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 5<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ 5
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