Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

What fractions can you find between the square roots of 56 and 58?

Can you hit the target functions using a set of input functions and a little calculus and algebra?

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

Can you work out the equations of the trig graphs I used to make my pattern?

Which line graph, equations and physical processes go together?

Draw the graph of a continuous increasing function in the first quadrant and horizontal and vertical lines through two points. The areas in your sketch lead to a useful formula for finding integrals.

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

You thought carefully about this problem and Luke was able to tell us about the shortest routes very convincingly.

There is still one unanswered question left, but most of this problem has been solved. Can anyone finish it off?

2009 was clearly an interesting year! Find out which mathematical fact about 2009 we found most interesting.

In this article, Jennifer Piggott talks about just a few of the problems with problems that make them such a rich source of mathematics and approaches to learning mathematics.

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

We asked what was the most interesting fact that you can find out about the number 2009. See the solutions that were submitted.