There are lots of different routes from A to B in this diagram:

routes

The idea is to work out the product of the numbers on these different routes from A to B. Let's say that in a route you are not allowed to visit a point more than once.

For example, we could have

3 \times 0.5

but we couldn't have

3 \times 2 \times 5 \times 4 \times 1 \times 0.1

because that route passes through A twice.

Which route or routes give the largest product?

Which route or routes give the smallest product?

Do you have any quick ways of working out the products each time?

[This problem is adapted from a SMILE Centre card. See www.smilemathematics.co.uk for information about their mathematics resources.]