SOLUTION: Find all sum of all possible 4 digit numbers that can be formed using th digits 2,4,5,6,7 and 8, with no repeated digits.

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Question 1123306: Find all sum of all possible 4 digit numbers that can be formed using th digits 2,4,5,6,7 and 8, with no repeated digits.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


In forming one of those 4-digit numbers, there are 6 choices for the first digit, then 5 for the second, 4 for the third, and 3 for the fourth. So the number of 4-digit numbers that can be formed is 6*5*4*3 = 360.

Imagine the list of those 360 numbers, ready to be added. Each of the 6 digits is used the same number of times; and each of them is used the same number of times in each column. That means that in each column of the list of the 360 numbers, each of the given digits is used 360/6 = 60 times.

The sum of the given digits is 2+4+5+6+7+8 = 32. So the sum of the digits in each column is 60*32 = 1920.

And then the sum of the 360 numbers is



You can also see the sum this way:



            245678

          + 245687

          +    ...

          + 876524

          + 876542

          --------

              1920

             1920

            1920

           1920

          1920

         1920

        -----------

         213333120


--------------------------------------------------------------

Thanks to tutor @ikleyn for pointing out my error....


I absentmindedly added 6-digit numbers instead of 4-digit numbers.... 

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
 .





            The solution by @greenestamps is not precisely correct.





            It should be edited - so,  I place that solution here with my correction.








In forming one of those 4-digit numbers, there are 6 choices for the first digit, then 5 for the second, 
4 for the third, and 3 for the fourth.  So the number of 4-digit numbers that can be formed is 6*5*4*3 = 360.


Imagine the list of those 360 numbers, ready to be added.  Each of the 6 digits is used the same number of times; 
and each of them is used the same number of times in each column.  That means that in each column of the list 
of the 360 numbers, each of the given digits is used 360/6 = 60 times.


The sum of the given digits is 2+4+5+6+7+8 = 32.  So the sum of the digits in each column is 60*32 = 1920.


And then the sum of the 360 numbers is


1920(1000+100+10+1) = 2133120            <<<---===  My editing is in THIS LINE.





Answer.    The sum is   2133120.   





 

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