Can you explain the strategy for winning this game with any target?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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.
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you find all the 4-ball shuffles?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Here is a chance to play a version of the classic Countdown Game.
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
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 moves.
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Train game for an adult and child. Who will be the first to make the train?
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.
Exchange the positions of the two sets of counters in the least possible number of moves
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.