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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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?
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
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.
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Think of a number, square it and subtract your starting number. Is
the number you’re left with odd or even? How do the images
help to explain this?
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.
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
An investigation that gives you the opportunity to make and justify
Find out what a "fault-free" rectangle is and try to make some of
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
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.
Can you explain how this card trick works?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Find the sum of all three-digit numbers each of whose digits is
This challenge asks you to imagine a snake coiling on itself.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Delight your friends with this cunning trick! Can you explain how
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
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.