Question 1133013
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(1) To get the maximum sum, the leading digits B, M, and D must be, in some order, the three largest given digits, 3, 8, and 9.<br>
(2) That means the other letter A has to be 1.<br>
So the three 3-digit numbers are 91?, 81?, and 31?.<br>
Again, to get the maximum sum, the units digits have to be as large as possible.  Since in each of the three numbers the digits are all different, the units digit of 91? can't be 9, so it can be at most 8; for the other two 3-digit numbers, the units digit can be 9.<br>
And that fits with the given three 3-digit numbers, because two of them have the same units digit.<br>
So D is 9 and M is 8; and that makes B 3.<br>
So the three numbers are 319, 819, and 918; their sum is 2056.