Being curious

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

Try out this number trick. What happens with different starting numbers? What do you notice?

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

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?