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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.
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.
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?
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'.
What can you see? What do you notice? What questions can you ask?
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?
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?
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?
Which of the following cubes can be made from these nets?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
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.
Weekly Problem 36 - 2007
Find the length along the shortest path passing through certain points on the cube.
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?
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.
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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.
What's the largest volume of box you can make from a square of paper?
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
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?
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
How many winning lines can you make in a three-dimensional version of noughts and crosses?
These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
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.
See if you can anticipate successive 'generations' of the two animals shown here.
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
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.
Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
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.
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.
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
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.
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?
We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
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?
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?
Can you find a rule which relates triangular numbers to square numbers?
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?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
What does Pythagoras' Theorem tell you about the radius of these circles?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
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?
Weekly Problem 9 - 2016
The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?
Can you make a tetrahedron whose faces all have the same perimeter?
The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.
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?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
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?
Show that all pentagonal numbers are one third of a triangular number.
A 3x8 rectangle is cut into two pieces... then rearranged to form a right-angled triangle. What is the perimeter of the triangle formed?
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?
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?
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?
How does the perimeter change when we fold this isosceles triangle in half?
Weekly Problem 34 - 2015
Four tiles are given. For which of them can three be placed together to form an equilateral triangle?
Stephen stops at Darlington on his way to Durham. At what time does he arrive at Durham?
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?
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?
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.
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Can you find an efficent way to mix paints in any ratio?
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?
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?
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?
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.
If you know the perimeter of a right angled triangle, what can you say about the area?
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?
Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?
Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.
A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.
A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
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.
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?
From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
When Andrew arrives at the end of the walkway, how far is he ahead of Bill?
In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?
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.
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?
Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.
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 ?
Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
Have you ever wondered what it would be like to race against Usain Bolt?
After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?
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.
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?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
To avoid losing think of another very well known game where the patterns of play are similar.