Counting

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of the creatures they could see. The creature looking to the West wrote 122. The creature looking to the East wrote 22. The creature looking to the South wrote 101. The creature looking to the North wrote 41. In which direction are the 2 Zios looking and in which directions are the 2 Zepts looking?

A game for two people, who take turns to move the counters. The player to remove the last counter from the board wins.

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

How many different ways can you arrange the officers in a square?

The interval 0 - 1 is marked into halves, quarters, eighths ... etc. Vertical lines are drawn at these points, heights depending on positions. What happens as this process goes on indefinitely?

Can you explain how this card trick works?

In how many ways can you give change for a ten pence piece?

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?

Weekly Problem 41 - 2009
At a cinema a child's ticket costs £4.20 and an adult's ticket costs £7.70. How much did is cost this group of adults and children to see a film?