Being curious

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Use your knowledge of place value to try to win this game. How will you maximise your score?

Can you use the clues to complete these 4 by 4 Mathematical Sudokus?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?