Use the differences to find the solution to this Sudoku.
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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.
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?
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.
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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.
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?
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Which set of numbers that add to 10 have the largest product?
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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?
If you move the tiles around, can you make squares with different coloured edges?
Can you maximise the area available to a grazing goat?
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?
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 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?
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?
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?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Explore the effect of combining enlargements.
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
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?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
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.
Is there an efficient way to work out how many factors a large number has?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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...
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?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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.
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?