Visualising and representing

problem

Tied Up

Age

14 to 16

Challenge level

How much of the field can the animals graze?
game

Jam

Age

14 to 16

Challenge level

A game for 2 players
game

Jam

Age

14 to 16

Challenge level

To avoid losing think of another very well known game where the patterns of play are similar.
problem

Just Rolling Round

Age

14 to 16

Challenge level

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?
problem

Platonic Planet

Age

14 to 16

Challenge level

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?
problem

Fermat's Poser

Age

14 to 16

Challenge level

Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.
problem

A Problem of Time

Age

14 to 16

Challenge level

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?
problem

Hypotenuse Lattice Points

Age

14 to 16

Challenge level

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?
problem

AMGM

Age

14 to 16

Challenge level

Can you use the diagram to prove the AM-GM inequality?
problem

A Tilted Square

Age

14 to 16

Challenge level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?