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Santa

Each of the letters D, A, Y, S, N, T, B, R and E represents a different non-zero digit. The following sum is true:
$$ \begin{array}{cccccc} D&A&D&D&Y\\ B&E&A&R&D&+\\ \hline S&A&N&T&A \end{array} $$
This has a unique solution, but I haven't found a way to find the solution without brute force. This less insightful sum is also true with the same values of the letters (and should allow you to find the values of the letters using logic alone):
$$ \begin{array}{ccccc} R&A&T&S\\ N&E&R&D&+\\ \hline S&A&N&E \end{array} $$

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