Being resourceful

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

The clues for this Sudoku are the product of the numbers in adjacent squares.

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

Can you do a little mathematical detective work to figure out which number has been wiped out?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

Which of these games would you play to give yourself the best possible chance of winning a prize?