Question 549512: Find the sum of all numbers greater than 10000 formed by using the digits 1,3,5,7,9, no digits being repeated in any number.
Answer- 6666600
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website! Here's why:
Suppose you had this long list of them to add:
13579
13597
13759
.....
.....
97351
97513
97531
------
There would be 5! or 120 numbers to add. Each vertical column of digits
contains an equal number of 1's, 3's, 5's, 7's and 9's. So since 120÷5
is 24, the sum of each column is 24×(1+3+5+7+9) = 600, The first column
represents 10000's, the 2nd column represents 1000's, etc. Therefore the
sum is:
600×10000 + 600×1000 + 600×100 + 600×10 + 600 =
600×(10000 + 1000 + 100 + 10 + 1) =
600×(11111) = 6666600
Edwin
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