Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Is there an efficient way to work out how many factors a large number has?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?
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?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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.
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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?
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?
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?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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...
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. . . .
Can you find rectangles where the value of the area is the same as the value of the perimeter?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
If you move the tiles around, can you make squares with different coloured edges?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Can you describe this route to infinity? Where will the arrows take you next?
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. . . .
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?
Explore the effect of combining enlargements.
Explore the effect of reflecting in two parallel mirror lines.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
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?
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?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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...
Can you maximise the area available to a grazing goat?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
A jigsaw where pieces only go together if the fractions are equivalent.
Which set of numbers that add to 10 have the largest product?
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?
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?