Find the sum of all possible combinations?
Given the four digits 1, 2, 3, and 4. If you generated every possible combination of the four digits, what would be the sum of all these combinations?
[For example, with the digits 1, 2 and 3; there are six combinations and the sum of these combinations is:
123 + 132 + 213 + 231 + 312 + 321 = 1332.
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1 solution
Moderator note:
Simple standard approach.
Lovely problem! Thanks!
There will be 4 ! = 2 4 such numbers. Six of them will have a 4 in the 1000 position, and another six will have a 3,2, or 1. Thus the sum of the 1000 positions of all 24 numbers is 6 ∗ 1 0 0 0 ∗ ( 1 + 2 + 3 + 4 ) = 6 0 0 0 0 . Likewise, the sums of the other three positions are 6000, 600, and 60, so that the overall sum is 6 6 6 6 0 .