6.2. 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.)
Answer: $1471+471+71+1=2014$.

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

## Grading Criteria:

+ fully justified solution

$\pm$ only the correct answer is provided or the correct answer with partial justifications

partially justified values for some letters, but the wrong answer is provided

- the problem is not solved or solved incorrectly