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. . . .
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...
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
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. . . .
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?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
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.
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?
What is the smallest number with exactly 14 divisors?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
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?
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?
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 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?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
Chris and Jo put two red and four blue ribbons in a box. They each
pick a ribbon from the box without looking. Jo wins if the two
ribbons are the same colour. Is the game fair?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Each of the following shapes is made from arcs of a circle of
radius r. What is the perimeter of a shape with 3, 4, 5 and n
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 find rectangles where the value of the area is the same as the value of the perimeter?
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?
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Here's a chance to work with large numbers...
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Use the differences to find the solution to this Sudoku.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
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?
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?
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?
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.
A jigsaw where pieces only go together if the fractions are
Explore the effect of reflecting in two parallel mirror lines.
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...