What must be added to the least number formed by the digits $0, 1, 3, 5, 7$ each only once to get the sum as the greatest number formed by the digits $0, 2, 4, 6, 8$ each only once?

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Solution

The least number formed by the digits $0, 1, 3, 5, 7$ each only once $= 10, 357$
The greatest number formed by the digits $0, 2, 4, 6, 8$ each only once $= 86, 420$
The difference of $86, 420$ and $10, 357$ is the required number.
$86420 - 10357 76063$
Hence, the required number is $76, 063 .$

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