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.
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?
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.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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
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?
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. . . .
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
How many different symmetrical shapes can you make by shading triangles or squares?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
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. . . .
What is the smallest number with exactly 14 divisors?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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 pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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.
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?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
Explore the effect of reflecting in two parallel mirror lines.
Can you describe this route to infinity? Where will the arrows take you next?
Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .
Can you work out the dimensions of the three cubes?
Why does this fold create an angle of sixty degrees?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Can you maximise the area available to a grazing goat?
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?
A plastic funnel is used to pour liquids through narrow apertures.
What shape funnel would use the least amount of plastic to
manufacture for any specific volume ?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Use the differences to find the solution to this Sudoku.
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?
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.
Explore the effect of combining enlargements.
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?
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
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
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...