In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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. . . .
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?
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 describe this route to infinity? Where will the arrows take you next?
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?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
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?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
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?
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?
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.
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.
Can you maximise the area available to a grazing goat?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Explore the effect of combining enlargements.
Can all unit fractions be written as the sum of two unit fractions?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
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?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
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?
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?
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 ?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
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?
What is the smallest number with exactly 14 divisors?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
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.
Can you work out the dimensions of the three cubes?
Can you find the area of a parallelogram defined by two vectors?
Use the differences to find the solution to this Sudoku.