Use the differences to find the solution to this Sudoku.
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?
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. . . .
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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 find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
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.
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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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 have only 40 metres of fencing available, what is the maximum area of land you can fence off?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
There are lots of different methods to find out what the shapes are worth - how many can you find?
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.
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you work out the dimensions of the three cubes?
Explore the effect of combining enlargements.
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. . . .
Explore the effect of reflecting in two parallel mirror lines.
Can you describe this route to infinity? Where will the arrows take you next?
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?
Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...
Find the decimal equivalents of the fractions one ninth, one ninety ninth, one nine hundred and ninety ninth etc. Explain the pattern you get and generalise.
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Which set of numbers that add to 10 have the largest product?
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?
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...
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 a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
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...
If you move the tiles around, can you make squares with different coloured edges?
Can you maximise the area available to a grazing goat?
Can all unit fractions be written as the sum of two unit fractions?
Can you find the area of a parallelogram defined by two vectors?
Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
A jigsaw where pieces only go together if the fractions are equivalent.
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?