Find The Sum Of All The Four Digits Numbers That Can Be Obtained By Using The Digits 1,2,3,4?

There are 4^4 = 256 numbers that can be formed, ranging from 1111 to 4444. Each digit will show in each position 256/4 = 64 times. Thus the sum of digits in any column is 64*(1+2+3+4) = 640
The sum of all the numbers is 1111*640 = 711,040.