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Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The letters $a, b, c, d, e$ and $f$ represent single digits and each letter represents a different digit. They satisfy the following equations: $a + b = d$ , $b + c = e$ and $d + e = f$ . Find all possible solutions for the values of $a, b, c, d, e$ and $f$ .

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