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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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Legs Eleven

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

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Football Sum

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

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.