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. . . .

There are nasty versions of this dice game but we'll start with the nice ones...

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?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!

There are six numbers written in five different scripts. Can you sort out which is which?

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.

A political commentator summed up an election result. Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.

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?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Investigate what happens when you add house numbers along a street in different ways.

Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?

Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Can you complete this jigsaw of the multiplication square?

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?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Dicey Operations for an adult and child. Can you get close to 1000 than your partner?

Look at some of the results from the Olympic Games in the past. How do you compare if you try some similar activities?

Find the exact difference between the largest ball and the smallest ball on the Hepta Tree and then use this to work out the MAGIC NUMBER!

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

Use the interactivities to complete these Venn diagrams.

These interactive dominoes can be dragged around the screen.

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?