2023 AIME II Problems/Problem 2
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Problem
Recall that a palindrome is a number that reads the same forward and backward. Find the greatest integer less than 
that is a palindrome both when written in base ten and when written in base eight, such as 
Solution
We have two cases:
- If the palindrome written in base eight has three digits, then it is at most
- If the palindrome written in base eight has four digits, then it is at least
To maximize the palindrome,
See also
| 2023 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
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