Copyright © University of Cambridge. All rights reserved.
The number may be divided up into 400 blocks of '12345'. The sum of the digits in each block is 15 and there are 400 blocks. Hence the sum of all 2000 digits is 400 x 15 = 6000.
Alternatively, the mean of each group of five digits is 3 and so the mean of the digits making up the number is 3. Therefore the sum is 2000x3 = 6000.
This problem is taken from the UKMT Mathematical Challenges.