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The four-digit number that reverses when multiplied by four

numbersdigitsreversalclassic

Find a four-digit number whose digits, when the number is multiplied by 4, come out in exactly reverse order. In symbols, ABCD × 4 = DCBA.

Then find the corresponding number for multiplying by 9.

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The first digit A must be small, since 4 × ABCD is still four digits. And the last digit D, multiplied by 4, must end in A. Those two facts pin down A and D quickly.

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