Use the differences to find the solution to this Sudoku.
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
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.
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
The sums of the squares of three related numbers is also a perfect
square - can you explain why?
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?
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?
Is there an efficient way to work out how many factors a large number has?
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?
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?
If a sum invested gains 10% each year how long before it has
doubled its value?
If the hypotenuse (base) length is 100cm and if an extra line
splits the base into 36cm and 64cm parts, what were the side
lengths for the original right-angled triangle?
Can you find the area of a parallelogram defined by two vectors?
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.
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 ?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
There are lots of different methods to find out what the shapes are worth - how many can you find?
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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. . . .
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
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?
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.
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. . . .
This shape comprises four semi-circles. What is the relationship
between the area of the shaded region and the area of the circle on
AB as diameter?
Explore the effect of combining enlargements.
Explore the effect of reflecting in two parallel mirror lines.
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?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Can you describe this route to infinity? Where will the arrows take you next?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
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?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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?
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?
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?