sum of the numbers

[kewltot]

1234
1342
1324
・
・
・
the addition problem above shows four of the 24 different integers that can be formed by each of the 1,2,3 and 4 exactly once in each integer. what is the sum of 24 integers?

[ace_gre]

Hi, Since there are 24 numbers, each of the digits 1, 2, 3 and 4 will appear in the units digit 6 times, ten's digit 6 times, hundred's digit 6 times and thousand's digit 6 times.

Now adding the unit's digit ==> 6*1 + 6*2 + 6*3 + 6*4 = 6 + 12 +18 + 24 = 60-------(1)
So the unit's digit of the sum = 0 and 6 is carried over.

Ten's digits will be same as 1 plus 6 carried over. so ten's digit addition is 66.
Ten's digit of the sum is 6 and 6 is carried over.

Following same logic for hundred's 6

Thousand's digit is 66.

So the final sum IMO is 66,660.