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UKMT Cayley Olympiad, 2019

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

In the addition shown, each of the letters $D$ , $O$ , $G$ , $C$ , $A$ and $T$ represents a different digit. $DOG + CAT = 1000$ What is the value of $D + O + G + C + A + T$ ?

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