The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
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?
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
Simple additions can lead to intriguing results...
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
Can you work out the dimensions of the three cubes?
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
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?
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?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
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?
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?
There are unexpected discoveries to be made about square numbers...
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Can you find the area of a parallelogram defined by two vectors?
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
If a sum invested gains 10% each year how long before it has doubled its value?
Explore the relationships between different paper sizes.
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
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.
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?
