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?
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.
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?
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
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?
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?
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.
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
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
11x11 square
Age
11 to 16
Challenge level
Here's a neat trick you can do with an 11 by 11 square...
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
Favourite
Pythagoras proofs
Age
11 to 16
Challenge level
Can you make sense of these three proofs of Pythagoras' Theorem?
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
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
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
Multiple surprises
Age
11 to 16
Challenge level
Sequences of multiples keep cropping up...
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.
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
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?
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.
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.
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?
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
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
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
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
Eulerian
Age
14 to 16
Challenge level
Weekly Problem 37 - 2014
Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?
Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?
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
Travelator
Age
14 to 16
Challenge level
When Andrew arrives at the end of the walkway, how far is he ahead of Bill?
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
Painted purple
Age
14 to 16
Challenge level
Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?
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
Favourite
Which is bigger?
Age
14 to 16
Challenge level
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
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
Pyramidal n-gon
Age
14 to 16
Challenge level
The base of a pyramid has n edges. What is the difference between the number of edges the pyramid has and the number of faces the pyramid has?
problem
Concrete calculation
Age
14 to 16
Challenge level
The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to make the concrete raft for the foundations?
problem
Tennis training
Age
14 to 16
Challenge level
After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?
problem
Favourite
Always perfect
Age
14 to 18
Challenge level
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
problem
Favourite
Partly painted cube
Age
14 to 16
Challenge level
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo 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
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?
problem
In or out?
Age
14 to 16
Challenge level
Weekly Problem 52 - 2014
Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?
Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?
problem
Favourite
Speeding boats
Age
14 to 16
Challenge level
Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
problem
Favourite
Pair products
Age
14 to 16
Challenge level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
problem
Slippage
Age
14 to 16
Challenge level
A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?
problem
Penta colour
Age
14 to 16
Challenge level
In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?
problem
Dicey directions
Age
14 to 16
Challenge level
An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?
problem
Trisected triangle
Age
14 to 16
Challenge level
Weekly Problem 34 - 2015
Four tiles are given. For which of them can three be placed together to form an equilateral triangle?
Four tiles are given. For which of them can three be placed together to form an equilateral triangle?
problem
Tilting triangles
Age
14 to 16
Challenge level
A right-angled isosceles triangle is rotated about the centre point
of a square. What can you say about the area of the part of the
square covered by the triangle as it rotates?
problem
Can you traverse it?
Age
14 to 18
Challenge level
How can you decide if a graph is traversable?
problem
Favourite
Perfectly square
Age
14 to 16
Challenge level
The sums of the squares of three related numbers is also a perfect square - can you explain why?
problem
Favourite
Bendy quad
Age
14 to 16
Challenge level
Four rods are hinged at their ends to form a convex quadrilateral.
Investigate the different shapes that the quadrilateral can take.
Be patient this problem may be slow to load.
problem
Favourite
Vector journeys
Age
14 to 18
Challenge level
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
problem
Escalator
Age
14 to 16
Challenge level
At Holborn underground station there is a very long escalator. Two
people are in a hurry and so climb the escalator as it is moving
upwards, thus adding their speed to that of the moving steps. ...
How many steps are there on the escalator?
problem
Favourite
Spotting the loophole
Age
14 to 16
Challenge level
A visualisation problem in which you search for vectors which sum
to zero from a jumble of arrows. Will your eyes be quicker than
algebra?
problem
Favourite
Quadratic patterns
Age
14 to 16
Challenge level
Surprising numerical patterns can be explained using algebra and diagrams...
problem
A tilted square
Age
14 to 16
Challenge level
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
problem
Vanishing point
Age
14 to 18
Challenge level
How can visual patterns be used to prove sums of series?
problem
Changing places
Age
14 to 16
Challenge level
Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves it
will take to move the red counter to HOME?
problem
Contact
Age
14 to 16
Challenge level
A circular plate rolls in contact with the sides of a rectangular
tray. How much of its circumference comes into contact with the
sides of the tray when it rolls around one circuit?
problem
Triangles within triangles
Age
14 to 16
Challenge level
Can you find a rule which connects consecutive triangular numbers?
problem
Favourite
Factorising with multilink
Age
14 to 16
Challenge level
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
problem
Making tracks
Age
14 to 16
Challenge level
A bicycle passes along a path and leaves some tracks. Is it
possible to say which track was made by the front wheel and which
by the back wheel?
problem
Favourite
Pythagoras perimeters
Age
14 to 16
Challenge level
If you know the perimeter of a right angled triangle, what can you say about the area?
problem
Overlap
Age
14 to 16
Challenge level
A red square and a blue square overlap. Is the area of the overlap always the same?
problem
Favourite
Back fitter
Age
14 to 18
Challenge level
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
problem
Favourite
Painted cube
Age
14 to 16
Challenge level
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?
problem
Favourite
Picture story
Age
14 to 16
Challenge level
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
problem
Triangles within squares
Age
14 to 16
Challenge level
Can you find a rule which relates triangular numbers to square numbers?
problem
Favourite
What's that graph?
Age
14 to 18
Challenge level
Can you work out which processes are represented by the graphs?
problem
Favourite
One and three
Age
14 to 16
Challenge level
Two motorboats travelling up and down a lake at constant speeds
leave opposite ends A and B at the same instant, passing each
other, for the first time 600 metres from A, and on their return,
400 metres from B. How long is the lake?
problem
One out one under
Age
14 to 16
Challenge level
Imagine a stack of numbered cards with one on top. Discard the top,
put the next card to the bottom and repeat continuously. Can you
predict the last card?
problem
Favourite
Surprising transformations
Age
14 to 16
Challenge level
I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?
problem
Tetrahedra tester
Age
14 to 16
Challenge level
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
problem
Proximity
Age
14 to 16
Challenge level
We are given a regular icosahedron having three red vertices. Show
that it has a vertex that has at least two red neighbours.
problem
Triangles within pentagons
Age
14 to 16
Challenge level
Show that all pentagonal numbers are one third of a triangular number.
problem
Favourite
Filling the gaps
Age
14 to 16
Challenge level
Which numbers can we write as a sum of square numbers?
problem
Favourite
Plus minus
Age
14 to 16
Challenge level
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
problem
The perforated cube
Age
14 to 16
Challenge level
A cube is made from smaller cubes, 5 by 5 by 5, then some of those
cubes are removed. Can you make the specified shapes, and what is
the most and least number of cubes required ?
problem
Favourite
Negatively triangular
Age
14 to 16
Challenge level
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
problem
Quadratic matching
Age
14 to 16
Challenge level
Can you match each graph to one of the statements?
article
When the angles of a triangle don't add up to 180 degrees
This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.