<p>Recall that a palindrome is a number that reads the same forward and backward. Find the greatest integer less than <img alt="$1000$" height="13" src="https://latex.artofproblemsolving.com/6/e/e/6ee927e1332358c96c62c277441c907c4f51057f.png" width="35" /> that is a palindrome both when written in base ten and when written in base eight, such as <img alt="$292 = 444_{\text{eight}}.$" height="19" src="https://latex.artofproblemsolving.com/8/e/d/8edc3a9c9a09fa20e4a27b51eb844c96e4f748b0.png" width="115" /></p>

Question No: 393

Recall that a palindrome is a number that reads the same forward and backward. Find the greatest integer less than $1000$ that is a palindrome both when written in base ten and when written in base eight, such as $292 = 444_{\text{eight}}.$

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Tags: Algebra Combinatorics

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