Reasoning, convincing and proving

Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?

Weekly Problem 21 - 2010
How many diagonals can you draw on this square...

Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?

Mr Ross tells truths or lies depending on the day of the week. Can you catch him out?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

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

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.