game
Pumpkin Patch
A game for two players based on a game from the Somali people of Africa. The first player to pick all the other's 'pumpkins' is the winner.
game
Seega
An ancient game for two from Egypt. You'll need twelve distinctive 'stones' each to play. You could chalk out the board on the ground - do ask permission first.
game
Alquerque
This game for two, was played in ancient Egypt as far back as 1400 BC. The game was taken by the Moors to Spain, where it is mentioned in 13th century manuscripts, and the Spanish name Alquerque derives from the Arabic El- quirkat. Watch out for being 'huffed'.
interactivity
Introducing NRICH TWILGO
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
problem
Like a Circle in a Spiral
Age
7 to 16
Challenge level
A cheap and simple toy with lots of mathematics. Can you interpret
the images that are produced? Can you predict the pattern that will
be produced using different wheels?
problem
Air Nets
Age
7 to 18
Challenge level
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
problem
Clocking off
Age
7 to 16
Challenge level
I found these clocks in the Arts Centre at the University of
Warwick intriguing - do they really need four clocks and what times
would be ambiguous with only two or three of them?
problem
Prime Magic
Age
7 to 16
Challenge level
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
problem
Favourite
Fruity Totals
Age
7 to 16
Challenge level
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
problem
Cubic Conundrum
Age
7 to 16
Challenge level
Which of the following cubes can be made from these nets?
article
Shaping the universe III - to infinity and beyond
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
problem
Charting more success
Age
11 to 16
Challenge level
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
problem
Favourite
Multiple Surprises
Age
11 to 16
Challenge level
Sequences of multiples keep cropping up...
problem
Favourite
Rhombus It
Age
11 to 16
Challenge level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.
game
Sprouts
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
problem
Favourite
What's it worth?
Age
11 to 16
Challenge level
There are lots of different methods to find out what the shapes are worth - how many can you find?
problem
Instant Insanity
Age
11 to 18
Challenge level
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.
problem
Favourite
Nine Colours
Age
11 to 16
Challenge level
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
problem
LOGO Challenge - Circles as animals
Age
11 to 16
Challenge level
See if you can anticipate successive 'generations' of the two
animals shown here.
problem
Favourite
Searching for mean(ing)
Age
11 to 16
Challenge level
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
problem
LOGO Challenge - Triangles-Squares-Stars
Age
11 to 16
Challenge level
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
problem
Favourite
Hamiltonian Cube
Age
11 to 16
Challenge level
Weekly Problem 36 - 2007
Find the length along the shortest path passing through certain points on the cube.
Find the length along the shortest path passing through certain points on the cube.
problem
Favourite
Cuboid Challenge
Age
11 to 16
Challenge level
What's the largest volume of box you can make from a square of paper?
problem
Favourite
Take Three From Five
Age
11 to 16
Challenge level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
problem
What is the question?
Age
11 to 16
Challenge level
These pictures and answers leave the viewer with the problem "What
is the Question". Can you give the question and how the answer
follows?
game
Sliding Puzzle
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.
problem
Who's who?
Age
11 to 16
Challenge level
Can you solve the clues to find out who's who on the friendship graph?
article
Ding Dong Bell
The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
problem
Favourite
Marbles in a box
Age
11 to 16
Challenge level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
problem
Triangles in the middle
Age
11 to 18
Challenge level
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.
problem
The Bridges of Konigsberg
Age
11 to 18
Challenge level
Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
problem
Favourite
Semi-regular Tessellations
Age
11 to 16
Challenge level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
problem
11x11 square
Age
11 to 16
Challenge level
Here's a neat trick you can do with an 11 by 11 square...
article
Shaping the universe I - planet Earth
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.
article
Shaping the universe II - the solar system
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
problem
Charting success
Age
11 to 16
Challenge level
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
problem
Favourite
Funny Factorisation
Age
11 to 16
Challenge level
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
problem
Favourite
Pythagoras Proofs
Age
11 to 16
Challenge level
Can you make sense of these three proofs of Pythagoras' Theorem?
problem
Favourite
Parallelogram It
Age
11 to 16
Challenge level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.
game
Yih or Luk tsut k'i or Three Men's Morris
Some puzzles requiring no knowledge of knot theory, just a careful
inspection of the patterns. A glimpse of the classification of
knots and a little about prime knots, crossing numbers and knot
arithmetic.
problem
Favourite
Charlie's delightful machine
Age
11 to 16
Challenge level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
problem
Out of the Window
Age
14 to 16
Challenge level
Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.
problem
Favourite
Three cubes
Age
14 to 16
Challenge level
Can you work out the dimensions of the three cubes?
problem
Cubic Covering
Age
14 to 16
Challenge level
A blue cube has blue cubes glued on all of its faces. Yellow cubes are then glued onto all the visible blue facces. How many yellow cubes are needed?
problem
Around and Back
Age
14 to 16
Challenge level
A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns around and heads back to the starting point where he meets the runner who is just finishing his first circuit. Find the ratio of their speeds.
problem
Packing 3D shapes
Age
14 to 16
Challenge level
What 3D shapes occur in nature. How efficiently can you pack these shapes together?
problem
Favourite
Vector walk
Age
14 to 18
Challenge level
Starting with two basic vector steps, which destinations can you reach on a vector walk?
problem
Curve Hunter
Age
14 to 18
Challenge level
This problem challenges you to sketch curves with different properties.
problem
Bike Shop
Age
14 to 16
Challenge level
If I walk to the bike shop, but then cycle back, what is my average speed?
problem
Favourite
Steel Cables
Age
14 to 16
Challenge level
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
problem
Favourite
Square Number Surprises
Age
14 to 16
Challenge level
There are unexpected discoveries to be made about square numbers...
problem
Facial Sums
Age
14 to 16
Challenge level
Can you make the numbers around each face of this solid add up to the same total?
problem
Centre Square
Age
14 to 16
Challenge level
What does Pythagoras' Theorem tell you about the radius of these circles?
problem
Just rolling round
Age
14 to 16
Challenge level
P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
of P?
problem
Bus Stop
Age
14 to 16
Challenge level
Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant and in the ratio 5 to 4. The buses travel to and fro between the towns. What milestones are at Shipton and Veston?
problem
Favourite
Summing geometric progressions
Age
14 to 18
Challenge level
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
problem
Favourite
Dating made Easier
Age
14 to 16
Challenge level
If a sum invested gains 10% each year how long before it has
doubled its value?
problem
Favourite
Puzzling Place Value
Age
14 to 16
Challenge level
Can you explain what is going on in these puzzling number tricks?
problem
Summing squares
Age
14 to 16
Challenge level
Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?
game
Jam
To avoid losing think of another very well known game where the patterns of play are similar.
problem
Folding in Half
Age
14 to 16
Challenge level
How does the perimeter change when we fold this isosceles triangle in half?
problem
Coke machine
Age
14 to 16
Challenge level
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
problem
Inside Out
Age
14 to 16
Challenge level
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you can colour every face of all of the smaller cubes?
problem
Favourite
Doesn't add up
Age
14 to 16
Challenge level
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
problem
Favourite
Hollow Squares
Age
14 to 16
Challenge level
Which armies can be arranged in hollow square fighting formations?
problem
Gnomon dimensions
Age
14 to 16
Challenge level
These gnomons appear to have more than a passing connection with
the Fibonacci sequence. This problem ask you to investigate some of
these connections.
problem
Favourite
A question of scale
Age
14 to 16
Challenge level
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
game
Wari
This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?
problem
Favourite
Terminology
Age
14 to 16
Challenge level
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
problem
Packing Boxes
Age
14 to 16
Challenge level
Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.
problem
Just Opposite
Age
14 to 16
Challenge level
A and C are the opposite vertices of a square ABCD, and have
coordinates (a,b) and (c,d), respectively. What are the coordinates
of the vertices B and D? What is the area of the square?
problem
Sliced
Age
14 to 16
Challenge level
An irregular tetrahedron has two opposite sides the same length a
and the line joining their midpoints is perpendicular to these two
edges and is of length b. What is the volume of the tetrahedron?
problem
Favourite
Double Trouble
Age
14 to 16
Challenge level
Simple additions can lead to intriguing results...
problem
Fermat's Poser
Age
14 to 16
Challenge level
Find the point whose sum of distances from the vertices (corners)
of a given triangle is a minimum.
problem
Rectangle Rearrangement
Age
14 to 16
Challenge level
A 3x8 rectangle is cut into two pieces... then rearranged to form a right-angled triangle. What is the perimeter of the triangle formed?
problem
Semicircular Design
Age
14 to 16
Challenge level
Weekly Problem 9 - 2016
The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?
The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?
problem
Newspaper Sheets
Age
14 to 16
Challenge level
From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?
problem
Building Tetrahedra
Age
14 to 16
Challenge level
Can you make a tetrahedron whose faces all have the same perimeter?
problem
Circuit training
Age
14 to 16
Challenge level
Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?
problem
A Problem of time
Age
14 to 16
Challenge level
Consider a watch face which has identical hands and identical marks
for the hours. It is opposite to a mirror. When is the time as read
direct and in the mirror exactly the same between 6 and 7?
problem
Travelling by Train
Age
14 to 16
Challenge level
Stephen stops at Darlington on his way to Durham. At what time does he arrive at Durham?
problem
Favourite
Iff
Age
14 to 18
Challenge level
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
problem
Favourite
At right angles
Age
14 to 16
Challenge level
Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
problem
Favourite
Pick's Theorem
Age
14 to 16
Challenge level
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
problem
Favourite
Speed-time problems at the Olympics
Age
14 to 16
Challenge level
Have you ever wondered what it would be like to race against Usain Bolt?
problem
Something in Common
Age
14 to 16
Challenge level
A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
problem
Hypotenuse Lattice points
Age
14 to 16
Challenge level
The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
problem
Oldest and Youngest
Age
14 to 16
Challenge level
Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?
problem
Tetra Square
Age
14 to 18
Challenge level
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
problem
Building Gnomons
Age
14 to 16
Challenge level
Build gnomons that are related to the Fibonacci sequence and try to
explain why this is possible.
problem
Favourite
Mystic Rose
Age
14 to 16
Challenge level
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
problem
Corridors
Age
14 to 16
Challenge level
A 10x10x10 cube is made from 27 2x2 cubes with corridors between
them. Find the shortest route from one corner to the opposite
corner.
problem
Favourite
Which is cheaper?
Age
14 to 16
Challenge level
When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
problem
3D Treasure Hunt
Age
14 to 18
Challenge level
Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
problem
Relative Time
Age
14 to 16
Challenge level
Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?
problem
Star Gazing
Age
14 to 16
Challenge level
Find the ratio of the outer shaded area to the inner area for a six
pointed star and an eight pointed star.
problem
Twelve Cubed
Age
14 to 16
Challenge level
A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?