Finding the Number of Currents in a Circuit: Tips and Intuition

[oneplusone]

For the following circuit:

How would you deduce the number of currents there are?
I am having trouble predicting how many are there (i am convinced there are 3).

Also, in general, what are some tips for finding how many currents there are?

 

[ehild]

Choose a current flowing along any path between two nodes.
Yes, there are three in the circuit shown.

ehild