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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.
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'.
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?
What can you see? What do you notice? What questions can you ask?
Which of the following cubes can be made from these nets?
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?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Weekly Problem 36 - 2007
Find the length along the shortest path passing through certain points on the cube.
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?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
See if you can anticipate successive 'generations' of the two animals shown here.
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?
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.
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.
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.
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?
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.
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
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?
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
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.
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
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.
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.
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.
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?
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?
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?
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?
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?
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.
After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?
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?
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 visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?
From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?
Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?
There are unexpected discoveries to be made about square numbers...
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.
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?
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.
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?
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?
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?
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?
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.
Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.
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?
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?
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?
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?