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Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

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Can you explain the strategy for winning this game with any target?

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Is there an efficient way to work out how many factors a large number has?

Stair Climb

Age 11 to 14 Short
Challenge Level

Boris, Spike and Percival are going to race up the 99 steps that lead from the beach to the car park at the top of the cliff.

Boris can run up five steps in the same time as Spike can run up four steps, which is the same time as Percival can run up three steps.

It is agreed that Boris starts from the bottom, Spike starts 21 steps up and Percival 38 steps up.

If they all start at the same time, in what order will they reach the top?

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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.