Find all solutions to the puzzle: ARKA + RKA + KA + A = 2014. (Different letters correspond to different digits, and the same letters correspond to the same digits.)

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Since in the word ARKA the digit in the thousands place is A, then A = 1 or 2. Moreover, A + A + A + A ends in 4, so $\mathrm{A}=1$. Since $\mathrm{K}+\mathrm{K}+\mathrm{K}$ ends in 1, then $\mathrm{K}=7$. Since $\mathrm{P}+\mathrm{P}+2=10$, then $\mathrm{P}=4$.

## Answer

$1471+471+71+1=2014$.

## Problem