AB * CD = BA * DC

Number Theory Level 5

We know that the order of digits in a number matter, and we cannot randomly swap them around. Most of the time,

\[ \overline{AB} \times \overline{CD} \neq \overline{BA} \times \overline{DC} .\]

How many ordered tuples of non-zero digits \( (A, B, C, D) \) are there such that

\[ \overline{AB} \times \overline{CD} = \overline{BA} \times \overline{DC} ? \]


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