Visualising and representing

problem

Semicircular Design

Age

14 to 16

Challenge level

Weekly Problem 9 - 2016
The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?
problem

Quadratic Matching

Age

14 to 16

Challenge level

Can you match each graph to one of the statements?
game

Wari

Age

14 to 16

Challenge level

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?
problem

Just Opposite

Age

14 to 16

Challenge level

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?
problem

Building Tetrahedra

Age

14 to 16

Challenge level

Can you make a tetrahedron whose faces all have the same perimeter?
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

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

Gnomon Dimensions

Age

14 to 16

Challenge level

These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.
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

Corridors

Age

14 to 16

Challenge level

A 10×10×10 cube is made from 27 2×2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.