The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Can you find a way to identify times tables after they have been shifted up or down?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Join pentagons together edge to edge. Will they form a ring?

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Play around with sets of five numbers and see what you can discover about different types of average...

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Which armies can be arranged in hollow square fighting formations?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.