Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Delight your friends with this cunning trick! Can you explain how
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.
Can you explain how this card trick works?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
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.
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?
Crosses can be drawn on number grids of various sizes. What do you
notice when you add opposite ends?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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
Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat. . . .
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Replace each letter with a digit to make this addition correct.
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
What are the missing numbers in the pyramids?
Three dice are placed in a row. Find a way to turn each one so that
the three numbers on top of the dice total the same as the three
numbers on the front of the dice. Can you find all the ways to. . . .
Find the sum of all three-digit numbers each of whose digits is
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
An environment which simulates working with Cuisenaire rods.
Find out about Magic Squares in this article written for students. Why are they magic?!
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
This is an adding game for two players.
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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 challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Here is a chance to play a version of the classic Countdown Game.
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
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?