Find the sum of all three-digit numbers each of whose digits is odd.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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 happens?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Can you explain the strategy for winning this game with any target?
Can you explain how this card trick works?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Delight your friends with this cunning trick! Can you explain how it works?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Here are two kinds of spirals for you to explore. What do you notice?
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.
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Got It game for an adult and child. How can you play so that you know you will always win?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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 all the ways to get 15 at the top of this triangle of numbers?
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
This activity involves rounding four-digit numbers to the nearest thousand.
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
Can you tangle yourself up and reach any fraction?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
How many moves does it take to swap over some red and blue frogs? Do you have a method?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
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.
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
It would be nice to have a strategy for disentangling any tangled ropes...
Find out what a "fault-free" rectangle is and try to make some of your own.