Counting

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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

Can you work out how to win this game of Nim? Does it matter if you go first or second?

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?

Can you find a path from a number at the top of this network to the bottom which goes through each number from 1 to 9 once and once only?

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.