Sum of Three-Digit Integers

What is the sum of all the positive three-digit integers that can be formed from the digits 2,3,5,6, and 7? Note that the same digit can appear more than once.
Source: NCTM Mathematics Teacher, February 2006

SOLUTION
We can make 5\times 5\times 5=125 different three-digit integers from 2,3,5,6, and 7
222\: 223\: 225\: 226\: 227\:\cdots
Since each integer has 3 digits, we have a total of 125\times 3=375 digits which we are going to distribute evenly among 3 columns: the 100 column, the 10 column, and the unit column. Thus, each column has 375/3=125 digits.
If we divide the 125 digits evenly among the 2,3,5,6, and 7, each digit will appear 125/5=25 times in each column.
Sum of each column equals
25(2+3+5+6+7)=575
When we allow for place value, the sum of the integers equals
575(100)+575(10)+575=63825

Answer: 63825

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About mvtrinh

Retired high school math teacher.
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