What is the sum of all the digits in all the integers from one to
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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.