Why does this fold create an angle of sixty degrees?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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. . . .
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...
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.
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
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?
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?
An aluminium can contains 330 ml of cola. If the can's diameter is
6 cm what is the can's height?
There are lots of different methods to find out what the shapes are worth - how many can you find?
All CD Heaven stores were given the same number of a popular CD to
sell for £24. In their two week sale each store reduces the
price of the CD by 25% ... How many CDs did the store sell at. . . .
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?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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?
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?
Explore when it is possible to construct a circle which just
touches all four sides of a quadrilateral.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
The diagonals of a trapezium divide it into four parts. Can you
create a trapezium where three of those parts are equal in area?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
How many different symmetrical shapes can you make by shading triangles or squares?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
Use the differences to find the solution to this Sudoku.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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.
What is the smallest number with exactly 14 divisors?
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?
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
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. . . .
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
A square of area 40 square cms is inscribed in a semicircle. Find
the area of the square that could be inscribed in a circle of the
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?
Explore the effect of reflecting in two parallel mirror lines.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Explore the effect of combining enlargements.
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
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?