### Digit Sum

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

### Football Sum

Find the values of the nine letters in the sum: FOOT + BALL = GAME

### Cycle It

Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total.

# Tick Tock

##### Stage: 3 Short Challenge Level:

Tick's watch runs 2 minutes per hour too slow. Tock's watch runs 1 minute per hour too fast. They set them to the same time at noon on Sunday. The next time they met, one of the watches was one hour ahead of the other. What was the earliest time this could have been?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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