Find the sum
What is the sum of all the combinations of the digits 2, 3, 5, 8 and 9?
For example, the combinations of the digits 1 and 2 are 12 and 21. There are 2 combinations, and the sum of their combinations is .
The answer is 7199928.
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1 solution
There are a total of 5 ! = 1 2 0 combinations.
Considering the combinations,
2 3 5 8 9
2 3 5 9 8
2 3 9 5 8
2 3 9 8 5
2 3 8 9 5
2 3 8 5 9
2 5 3 8 9
2 5 3 9 8
2 5 9 3 8
2 5 9 8 3
2 5 8 3 9
2 5 8 9 3
2 8 3 5 9
2 8 3 9 5
2 8 5 3 9
2 8 5 9 3
2 8 9 3 5
2 8 9 5 3
2 9 3 5 8
2 9 3 8 5
2 9 5 3 8
2 9 5 8 3
2 9 8 3 5
2 9 8 5 3
3 2 5 8 9 , and so on ...
If we continue this until the 1 2 0 t h combination, we will notice that each digit appears in each column 2 4 times.
So each column adds up to 2 4 ( 2 + 3 + 5 + 8 + 9 ) = 6 4 8
Therefore the sum is 6 4 8 ( 1 + 1 0 + 1 0 0 + 1 0 0 0 + 1 0 0 0 0 ) = 7 1 9 9 9 2 8