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?
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.
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 notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Can you see how to build a harmonic triangle? Can you work out the next two rows?
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.
Can all unit fractions be written as the sum of two unit fractions?
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?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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
Explore the effect of reflecting in two parallel mirror lines.
Explore the effect of combining enlargements.
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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. . . .
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?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
Use the differences to find the solution to this Sudoku.
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?
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 smallest number with exactly 14 divisors?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
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?
There is a particular value of x, and a value of y to go with it,
which make all five expressions equal in value, can you find that
x, y pair ?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Can you describe this route to infinity? Where will the arrows take you next?
A circle of radius r touches two sides of a right angled triangle,
sides x and y, and has its centre on the hypotenuse. Can you prove
the formula linking x, y and r?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
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 maximise the area available to a grazing goat?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you find the area of a parallelogram defined by two vectors?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
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?
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 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 sum invested gains 10% each year how long before it has
doubled its value?