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.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Delight your friends with this cunning trick! Can you explain how
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Can you explain how this card trick works?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
What are the missing numbers in the pyramids?
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?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
In the following sum the letters A, B, C, D, E and F stand for six
distinct digits. Find all the ways of replacing the letters with
digits so that the arithmetic is correct.
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
Replace each letter with a digit to make this addition correct.
Choose any three by three square of dates on a calendar page...
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
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?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
Find the sum of all three-digit numbers each of whose digits is
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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!
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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 article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
Here is a chance to play a version of the classic Countdown Game.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.