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.
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
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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?
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Can you find all the 4-ball shuffles?
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 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.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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.
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outline of this junk?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
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
Can you fit the tangram pieces into the outline of Mai Ling?
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 fit the tangram pieces into the outline of Little Ming?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
Can you fit the tangram pieces into the outlines of the chairs?
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?
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
Can you discover whether this is a fair game?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
You have 27 small cubes, 3 each of nine colours. Use the small
cubes to make a 3 by 3 by 3 cube so that each face of the bigger
cube contains one of every colour.
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you fit the tangram pieces into the outlines of the workmen?