<p>A number <img alt="$N$" height="14" src="https://latex.artofproblemsolving.com/f/c/9/fc97ef67268cd4e91bacdf12b8901d7036c9a056.png" width="18" /> has three digits when expressed in base <img alt="$7$" height="14" src="https://latex.artofproblemsolving.com/e/0/a/e0a0db32027a732ac57d37ef2ae9bb150f65b108.png" width="11" />. When <img alt="$N$" height="14" src="https://latex.artofproblemsolving.com/f/c/9/fc97ef67268cd4e91bacdf12b8901d7036c9a056.png" width="18" /> is expressed in base <img alt="$9$" height="14" src="https://latex.artofproblemsolving.com/b/f/2/bf2c9074b396e3af0dea52d792660eea1c77f10f.png" width="11" /> the digits are reversed. Then the middle digit is:</p> <p><img alt="$\text{(A) } 0\quad \text{(B) } 1\quad \text{(C) } 3\quad \text{(D) } 4\quad \text{(E) } 5$" height="17" src="https://latex.artofproblemsolving.com/8/e/6/8e60832e044842332e9ddfdeccc318a3f0df03b8.png" width="263" /></p>

Question No: 455

A number $N$ has three digits when expressed in base $7$ . When $N$ is expressed in base $9$ the digits are reversed. Then the middle digit is:

$\text{(A) } 0\quad \text{(B) } 1\quad \text{(C) } 3\quad \text{(D) } 4\quad \text{(E) } 5$

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Tags: Number Theory

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