Is there an efficient way to work out how many factors a large number has?
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
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.
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?
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?
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.
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
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...
The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?
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?
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.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?
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. . . .
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
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?
Use the differences to find the solution to this Sudoku.
A jigsaw where pieces only go together if the fractions are equivalent.
What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?
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?
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?
Which set of numbers that add to 10 have the largest product?
Here's a chance to work with large numbers...
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?
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...
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 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?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
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. . . .