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1993 AMC 12 #7 - Base-ten Representation

Source:

January 2, 2012
AMC

Problem Statement

The symbol RkR_k stands for an integer whose base-ten representation is a sequence of kk ones. For example, R3=111R_3=111, R5=11111R_5=11111, etc. When R24R_{24} is divided by R4R_4, the quotient Q=R24R4Q=\frac{R_{24}}{R_4} is an integer whose base-ten representation is a sequence containing only ones and zeros. The number of zeros in QQ is
<spanclass=′latex−bold′>(A)</span> 10<spanclass=′latex−bold′>(B)</span> 11<spanclass=′latex−bold′>(C)</span> 12<spanclass=′latex−bold′>(D)</span> 13<spanclass=′latex−bold′>(E)</span> 15 <span class='latex-bold'>(A)</span>\ 10 \qquad<span class='latex-bold'>(B)</span>\ 11 \qquad<span class='latex-bold'>(C)</span>\ 12 \qquad<span class='latex-bold'>(D)</span>\ 13 \qquad<span class='latex-bold'>(E)</span>\ 15
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