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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

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?

Consecutive Seven

Age 11 to 14 Challenge Level:
Consecutive numbers are numbers which follow each other when you are counting, for example, $4$, $5$, $6$, $7$ or $19$, $20$, $21$, $22$, $23$.

What is the total of all the numbers from $0$ to $20$?