Question

A path is traced from point A to point B by using the segments shown in the diagram. Paths are traced only upwards, to the right, or diagonally upwards. How many different paths can be traced from A to B?

Answer 1

Step-by-step answer:

If one is constrained to move to the right, or up, or diagonally upwards (i.e. remain in the first quadrant), then

there are three choices at A.

At the next position, whichever path one has taken, there are also three choices.

At the following position, there are no more choices.

Therefore, there are 3*3 = 9 different paths.