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What is the least positive difference between two three-digit numbers if one number has all the digits 2, 4, and 6, while the other has all the digits 1, 2, and 9?
If you're talking about the divisibility, the least you can get is 24 (2,4,6) and 18 (1,2,9). If you're to combine it, the 246 and 129 is the solution.
To see why this can't be smaller, notice to get something smaller the hundreds digits should be the same or differ by 1.
If they are the same, they must both be 2. so it just becomes the positive difference between a 4, 6 and a 9, 1. It is easy to see that that difference is 46-19=27.
Otherwise we need 2 _ _ (4,6) - 1 _ _ (2,9). The minimum difference is 246-191=55.
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