Question

If a, b, c, d, e, f, g, h are numbers from 1 to 8 and they are distinct, what will be the value of abcdefgh, which is an eight-digit number if abcd×2 = efgh?

Answer 1

any of {17283456, 17643528, 17823564, 18273654, 21784356, 23584716, 27185436, 28175634, 35647128, 35827164, 41768352, 43568712}

Explanation:

You want an 8-digit number abcdefgh such that abcd×2 = efgh and the digits form the set {1, 2, 3, 4, 5, 6, 7, 8}.

Trial and error

Using an exhaustive search, we found 12 solutions to this question:

17283456, 17643528, 17823564, 18273654,

21784356, 23584716, 27185436, 28175634,

35647128, 35827164, 41768352, 43568712

Digit 'a' cannot be greater than 4, otherwise efgh would not be a 4-digit number. And digit 'h' must be an even digit. These restrictions cut the search space substantially.

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