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The nine digit number

Let the number be abcd5fghi. It's clear that the fifth digit has to be 5. b, d, f and h are elements of {2,4,6,8} and the remaining a, c, g and i are elements of {1,3,7,9}. So there are at most 24 * 24 = 576 possibilities. But we can limit these possibilities drastic. 2c + d has to be divisible by 4, 4d + 20 + 4f by 6 and 2g + h by 4. Now you will find only one possibility: 381654729


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