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Schools Mathematics Grand Challenge


A new hotel has 40 floors, which are numbered from 1 to 40, and a nice new shiny elevator. The elevator travels at a constant speed and takes exactly 7 seconds to go from the floor 1 to floor 6 (if it does not stop in between). How long does it take to go from floor 1 to the floor 36 (again if it does not stop in between)?


Mary has recently purchased a second-hand car for less than 5000 euros. The garage will allow her to pay for the car in ten different ways. She can pay for the car in one single payment, or in 2, 3, 4, 5, 6, 7, 8, 9 or 10 equal instalments. For example, if the car costs 1,000 euro (which it doesn't!) she could make 1 payment of 1,000 euro, 2 payments of 500 euro, 3 payments of 333.33 euro, 4 payments of 250 euro and so on.

However, Mary has noticed that, whichever payment scheme she chooses, all of the amounts she pays are whole numbers of euros (for example, a payment of 333.33 can never happen). How much did Mary's car cost?


What is the only two digit number (i.e., a number between 10 and 99 inclusive) with the following property?

If you add its digits together and multiply the answer by 6, you recover the original number.


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