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?

Largest Number

Age 11 to 14 Challenge Level

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like. You can only use each digit once.
For example: 34 x 2 = 68 or 3 + 4 ^{2} = 19