Two boats travel up and down a lake. Can you picture where they
will cross if you know how fast each boat is travelling?
Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?
Can you see how this picture illustrates the formula for the sum of
the first six cube numbers?
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?
Explore the lattice and vector structure of this crystal.
Use the diagram to investigate the classical Pythagorean means.
Farey sequences are lists of fractions in ascending order of
magnitude. Can you prove that in every Farey sequence there is a
special relationship between Farey neighbours?
Rajeev and Christian both explained their thinking about this
probability problem very clearly.
Go to last month's problems to see more solutions.
In this article, we look at solids constructed using symmetries of
An article introducing continued fractions with some simple puzzles for the reader.
A java applet that takes you through the steps needed to solve a
Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.