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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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.
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
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?
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.
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?
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...
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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 know a quick way to check if a number is a multiple of two? How about three, four or six?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
What is the smallest number with exactly 14 divisors?
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. . . .
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?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
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?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
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. . . .
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
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?
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.
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?
The area of a square inscribed in a circle with a unit radius is,
satisfyingly, 2. What is the area of a regular hexagon inscribed in
a circle with a unit radius?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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?
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Use the differences to find the solution to this Sudoku.
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.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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. . . .
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Can you describe this route to infinity? Where will the arrows take you next?
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?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
How many different symmetrical shapes can you make by shading triangles or squares?
Can all unit fractions be written as the sum of two unit fractions?
Explore the effect of combining enlargements.