Nim-7 game for an adult and child. Who will be the one to take the last counter?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
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
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.
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?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Got It game for an adult and child. How can you play so that you know you will always win?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
What would be the smallest number of moves needed to move a Knight
from a chess set from one corner to the opposite corner of a 99 by
99 square board?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
A collection of games on the NIM theme
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Imagine a large cube made from small red cubes being dropped into a
pot of yellow paint. How many of the small cubes will have yellow
paint on their faces?
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
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.
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?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
This challenge asks you to imagine a snake coiling on itself.
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
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Here are two kinds of spirals for you to explore. What do you notice?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Find out what a "fault-free" rectangle is and try to make some of
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?