You Only Have Their Sums

Algebra Level 4

There are n3n \geq 3 people sitting in a circle, and each person is thinking of a number. Every consecutive pair announces the sum of their numbers (but not the individual numbers). For example, if there are three people with numbers a,b a, b and c c in that order, the three sums announced are a+b,b+c, a + b, b + c, and c+a. c + a .

For what values of nn can an outsider deduce all of the individual numbers?

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