Worms

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Greetings

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.

Number Lines in Disguise

Age 7 to 14Challenge Level
When you get stuck, here are some questions that you could use to help you get unstuck.
• Can you find the value of any of the unmarked points on the line?
• Can you find (approximately) where $0$ would be?
• Do you have a strategy that works for Level 1? If so, could you adapt it for the higher levels?