Digits

What is the sum of all the digits in all the integers from one to one million?

Don’t do a lot of tedious adding up – think mathematically!

Note: the digits in the integers from one to ten add up to 46
(not 55 because 10 contributes only 1 to this sum.)

Hint: Let a million stand alone.

Now introduce zero.

Every number except one million has a special partner.

Click here to download the DIGITS worksheet.

Click here for the Notes for Teachers.

This problem is adapted from the NRICH task Digit Sum with permission of the University of Cambridge. All rights reserved.