Difference between revisions of "2024 AIME II Problems/Problem 2"

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==Problem==
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A list of positive integers has the following properties:
 
A list of positive integers has the following properties:
  
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Find the sum of the squares of all the items in the list.
 
Find the sum of the squares of all the items in the list.
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==Solution 1==

Revision as of 19:37, 8 February 2024

Problem

A list of positive integers has the following properties:

$\bullet$ The sum of the items in the list is $30$.

$\bullet$ The unique mode of the list is $9$.

$\bullet$ The median of the list is a positive integer that does not appear in the list itself.

Find the sum of the squares of all the items in the list.

Solution 1