A certain insect is moving along the side of the pentagonal pyramid of the figure below.
When it started to move from the vertex A and come back to the vertex A again, how many ways are there on condition it never pass through the vertex twice and side passing through once ?
When it started to move from the vertex A and come back to the vertex A again, how many ways are there on condition it never pass through the vertex twice and side passing through once ?
Answer
Then there are two ways whether it rotates in the clockwise or counterclockwise direction.
In addition, there are four ways going back to A when it comes to which vertex.
In total, there are 40 ways by the calculation of 5 × 2 × 4 = 40.
40 ways
Solution
There are five ways starting from A to each of B,C,D,E,F.
Then there are two ways whether it rotates in the clockwise or counterclockwise direction.
In addition, there are four ways going back to A when it comes to which vertex.
In total, there are 40 ways by the calculation of 5 × 2 × 4 = 40.
