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?
Which of these games would you play to give yourself the best possible chance of winning a prize?
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. . . .
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
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's a chance to work with large numbers...
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?
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.
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?
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 pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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 number. . . .
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
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.
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.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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?
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 find rectangles where the value of the area is the same as the value of the perimeter?
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. . . .
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
Triangle ABC is isosceles while triangle DEF is equilateral. Find
one angle in terms of the other two.
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 jigsaw where pieces only go together if the fractions are
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
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...
What is the smallest number with exactly 14 divisors?
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.
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 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?
How many different symmetrical shapes can you make by shading triangles or squares?
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?
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?
Use the differences to find the solution to this Sudoku.
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?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
Explore the effect of reflecting in two parallel mirror lines.
Explore the effect of combining enlargements.