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Multiplication Squares

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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What's in the Box?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Turning Cogs

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
Do both cogs turn in the same direction?
With two cogs that have five teeth, will the marked tooth on one cog eventually fit in every gap of the other cog as they turn? Why or why not?
What happens if you pick a cog with five teeth and a cog with 6 teeth?