Difference between revisions of "2023 AIME II Problems/Problem 2"

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== Solution ==
 
== Solution ==
  
We have two cases:
 
<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,
 
  
  

Revision as of 15:24, 16 February 2023

Problem

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 $292 = 444_{\text{eight}}.$

Solution

See also

2023 AIME II (ProblemsAnswer KeyResources)
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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