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?

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

Which of these games would you play to give yourself the best possible chance of winning a prize?

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?

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

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

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?

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

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

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.

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?

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 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?

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

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

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?

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

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

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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

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.

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

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?

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

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

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

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

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. . . .

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?

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

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

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

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

A jigsaw where pieces only go together if the fractions are equivalent.

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.

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

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?

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...

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?

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

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?

Is there an efficient way to work out how many factors a large number has?

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

Explore the effect of reflecting in two parallel mirror lines.