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Aside from the 2 trivial answers, 0000x0=0000 and 1111x1=1111, there is one other answer. 1089*9=9801.

You find C & E pretty quickly, as running through the digits 2-9 yields either impossible situations or results exceeding 4 digits. It takes similar trial and error to deduce the other two digits such that it works out.

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