# You Only Have Their Sums

Algebra Level 4

There are $$n \geq 3$$ 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 $$a, b$$ and $$c$$ in that order, the three sums announced are $$a + b, b + c,$$ and $$c + a .$$

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

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