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Digit Sum

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

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Football Sum

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

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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: Challenge Level:1
8 am on Monday.

Each hour, Tock's watch gains three minutes on Tick's watch. It will, therefore, take 20 hours before it is one hour ahead of it.

This problem is taken from the UKMT Mathematical Challenges.