Being resourceful

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

The number in the square is the mean of the four numbers surrounding it. Can you find the missing numbers? 

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

How did the the rotation robot make these patterns?

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.

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

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?

What's the largest volume of box you can make from a square of paper?