6 positive integers wanted
Source: XII May Olympiad (Olimpiada de Mayo) 2006 L2 P3
September 19, 2022
combinatoricsnumber theory
Problem Statement
Write a positive integer in each box so that:
All six numbers are different.
The sum of the six numbers is .
If each number is multiplied by its neighbor (in a clockwise direction) and the six results of those six multiplications are added, the smallest possible value is obtained.
Explain why a lower value cannot be obtained.
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