Question

The task for the 8th grade :The digits in 5512 are rearranged to form all possible 4-digit positive integers. Find the last three digits of the sum of all such positive integers.

Answer 1

The 4 digit positive numbers from 5512 are:

$\mleft\lbrace5512,5521,1255,2155,1552,2551,1525,2515,5215,5125,5152,5251\mright\rbrace$

The sum of all the numbers will be:

$43329$

So the last three digits of the sum is 329.

Another way to do it is to add the three digits of the 4 digit numbers as shown below:

$\begin{gathered} 512+521+255+155++552+551+525+515+215+125+152+251 \\ =4329 \end{gathered}$

So the last digits is 329.