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Route Product

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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 $3\times0.5$ but we couldn't have $3\times2\times5\times4\times1\times 0.1$ 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.]