What is the smallest number with exactly 14 divisors?
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 rectangles where the value of the area is the same as the value of the perimeter?
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.
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...
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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. . . .
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
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?
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.
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. . . .
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Can you maximise the area available to a grazing goat?
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?
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 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.
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?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
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?
Use the differences to find the solution to this Sudoku.
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 jigsaw where pieces only go together if the fractions are
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Think of two whole numbers under 10. Take one of them and add 1.
Multiply by 5. Add 1 again. Double your answer. Subract 1. Add your
second number. Add 2. Double again. Subtract 8. Halve this. . . .
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?
Triangle ABC is isosceles while triangle DEF is equilateral. Find
one angle in terms of the other two.
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.
The Egyptians expressed all fractions as the sum of different unit
fractions. The Greedy Algorithm might provide us with an efficient
way of doing this.
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
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.
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
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. . . .
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
Start with two numbers. This is the start of a sequence. The next
number is the average of the last two numbers. Continue the
sequence. What will happen if you carry on for ever?
Can you describe this route to infinity? Where will the arrows take you next?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?