# Mistakes give rise to problems

**Logic**Level 5

\[ \large{\begin{array}{cccccc} & & & a & b & c&d\\ +& & & b & c & d & a \\ \hline && & & & & \phantom0&\\ \hline \end{array}} \qquad \qquad \large{\begin{array}{cccccc} & & & d & c & b &a \\ +& & & c& b & a & d \\ \hline && & & & \phantom0 &\\ \hline \end{array}} \]

If \(a,b,c\) and \(d\) are **not necessarily** distinct single-digit positive integers so that the result of both additions is the same, find the number of possible quadruples \((a,b,c,d) \).