The Better Bet
Stage: 4 Challenge Level: 
So which is the better bet? Both games cost £1 to play. Getting two heads and two tails for £3 or £2 for every six when three dice are rolled.
Tug of War
Stage: 1 Challenge Level:
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Property Chart
Stage: 3 Challenge Level:
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
Shapely Pairs
Stage: 3 Challenge Level:
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
The Birthday Bet
Stage: 4 Challenge Level:
The next ten people coming into a store will be asked their birthday. If the prize is £20, would you bet £1 that two of these ten people will have the same birthday ?
Sums of Squares
Stage: 5 Challenge Level:
Prove that 3 times the sum of 3 squares is the sum of 4 squares. Rather easier, can you prove that twice the sum of two squares always gives the sum of two squares?
Match the Matches
Stage: 2 Challenge Level:
Decide which charts and graphs represent the number of goals two football team scored in fifteen matches.
The Twelve Pointed Star Game
Stage: 2 Challenge Level:
Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?
First Connect Three
Stage: 2 and 3 Challenge Level:
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?
Snap
Stage: 1 Challenge Level:
Try this version of Snap with a friend - do you know the order of the days of the week?
Stop the Clock
Stage: 1 Challenge Level:
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Tug Harder!
Stage: 2 Challenge Level:
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
Diagonal Sums Sudoku
Stage: 2, 3 and 4 Challenge Level:
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
Product Sudoku
Stage: 3, 4 and 5 Challenge Level:
The clues for this Sudoku are the product of the numbers in adjacent squares.
Product Sudoku 2
Stage: 3, 4 and 5 Challenge Level:
Given the products of diagonally opposite cells - can you complete this Sudoku?
Incey Wincey Spider
Stage: 1 Challenge Level:
You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?
Name the Children
Stage: 1 Challenge Level:
Can you find out in which order the children are standing in this line?
Coin Tossing Games
Stage: 4 Challenge Level:
You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by. . . .
Stats Statements
Stage: 5 Challenge Level:
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Dice and Spinner Numbers
Stage: 2 Challenge Level:
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Hockey
Stage: 3 Challenge Level:
After some matches were played, most of the information in the table containing the results of the games was accidentally deleted. What was the score in each match played?
Counters
Stage: 2 Challenge Level:
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Got a Strategy for Last Biscuit?
Stage: 3, 4 and 5 Challenge Level:
Can you beat the computer in the challenging strategy game?
Tricky Track
Stage: 2 Challenge Level:
In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first? Is this what you would expect?
Four Go
Stage: 1 Challenge Level:
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
Twin Corresponding Sudoku III
Stage: 3 and 4 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
Polo Square
Stage: 2 Challenge Level:
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Twin Corresponding Sudokus II
Stage: 3 and 4 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
Wallpaper Sudoku
Stage: 3 and 4 Challenge Level:
A Sudoku that uses transformations as supporting clues.
Conway's Chequerboard Army
Stage: 3 Challenge Level:
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Taking Chances
Stage: 3 Challenge Level:
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance and is a shorter version of Taking Chances Extended.
Quadruple Clue Sudoku
Stage: 3 and 4 Challenge Level:
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
Balancing 2
Stage: 3 Challenge Level:
Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.
Bet You a Million
Stage: 4 Challenge Level:
Heads or Tails - the prize doubles until you win it. How much would you pay to play?
Quaternions and Rotations
Stage: 5 Challenge Level:
Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.
Shut the Box
Stage: 1 Challenge Level:
Try this old game that is very useful for so many arithmetical relationships.
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NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk
