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Age 11 to 14

Challenge Level

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Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on.

What would be the 1000th digit you would write down. In what number would it occur?

What number would contain the millionth digit?

When would you have written six for the 6000th time?

From a group of any 4 students in a class of 30, each has exchanged Christmas cards with the other three. Show that some students have exchanged cards with all the other students in the class. How many such students are there?

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?

A political commentator summed up an election result. Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.