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?

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.

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?

Even Up

Age 11 to 14 Challenge Level:

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?