Question

Aaron wrote down all the five- digit numbers which use only the digits. 1,2,8 and 9, with repetitions permitted. (1024 numbers in all, starting with 1111). Yuri added them all up ( correctly) to find the total. Without writing down all the numbers, find Yuri”s total.

Answer 1

Answer: Each digit appears in the units, tens, hundreds, thousands, and ten-thousands place 1024/4=256 times, so the sum of the digits in each place is:

Units: (1+2+8+9) x 256 = 3584

Tens: (1+2+8+9) x 256 x 10 = 35840

Hundreds: (1+2+8+9) x 256 x 100 = 358400

Thousands: (1+2+8+9) x 256 x 1000 = 3584000

Ten-thousands: (1+2+8+9) x 256 x 10000 = 35840000

Therefore, the total sum of all the numbers is:

3584 x (1 + 10 + 100 + 1000 + 10000) = 3584 x 11111 = 39,824,704

So Yuri's total is 39,824,704.

Explanation: