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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.
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?
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.
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'.
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?
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?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
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 second in a series of articles on visualising and modelling shapes in the history of astronomy.
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.
How many winning lines can you make in a three-dimensional version of noughts and crosses?
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
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 rhombus.
See if you can anticipate successive 'generations' of the two animals shown here.
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.
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.
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?
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?
Collect as many diamonds as you can by drawing three straight lines.
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?
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.
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.
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.
The sums of the squares of three related numbers is also a perfect square - can you explain why?
If I walk to the bike shop, but then cycle back, what is my average speed?
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?
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?
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 ?
Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
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?
Can you explain what is going on in these puzzling number tricks?
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?
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?
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?
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?
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?
Can you make the numbers around each face of this solid add up to the same total?
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?
Which armies can be arranged in hollow square fighting formations?
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
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?
These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.
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?
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?
Can you find a rule which connects consecutive triangular numbers?
If a sum invested gains 10% each year how long before it has doubled its value?
Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
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?
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?
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?
What 3D shapes occur in nature. How efficiently can you pack these shapes together?
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?
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?
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?
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?