Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Here is a chance to play a version of the classic Countdown Game.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
You have 5 darts and your target score is 44. How many different
ways could you score 44?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Different combinations of the weights available allow you to make different totals. Which totals can you make?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
An environment which simulates working with Cuisenaire rods.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?