There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

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

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?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Which set of numbers that add to 10 have the largest product?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

How many different symmetrical shapes can you make by shading triangles or squares?

If you move the tiles around, can you make squares with different coloured edges?

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

Explore the effect of combining enlargements.

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

Can you describe this route to infinity? Where will the arrows take you next?

Explore the effect of reflecting in two parallel mirror lines.

If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...