Reasoning, convincing and proving

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

In each of these games, you will need a little bit of luck, and your knowledge of place value to develop a winning strategy.

Can you use the clues to complete these 6 by 6 Mathematical Sudokus?

Can you use the clues to complete these 5 by 5 Mathematical Sudokus?

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

Can you use the clues to complete these 3 by 3 Mathematical Sudokus?

How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?

Do you agree with Badger's statements? Is Badger's reasoning watertight? Why or why not?

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?