Difference between revisions of "2023 AIME II Problems/Problem 2"
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== Solution == | == Solution == | ||
| − | If the palindrome written in base eight has three digits, then | + | We have two cases: |
| − | If the palindrome written in base eight has four digits, then | + | <ol style="margin-left: 1.5em;"> |
| + | <li>If the palindrome written in base eight has three digits, then it is at most <math>777_8 = 511.</math></li><p> | ||
| + | <li>If the palindrome written in base eight has four digits, then it is at least <math>1001_8 = 513.</math></li><p> | ||
| + | </ol> | ||
| + | To maximize the palindrome, | ||
| + | |||
| + | |||
== See also == | == See also == | ||
{{AIME box|year=2023|num-b=1|num-a=3|n=II}} | {{AIME box|year=2023|num-b=1|num-a=3|n=II}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 16:17, 16 February 2023
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
