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Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.


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?

Writ Large

Age 11 to 14 Challenge Level:

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?