vibhav wrote:

An ant is clinging to one corner of a box in the shape of a cube. The ant wants to get to the most distant corner of the box by crawling only along the edges of the cube and without ever revisiting a place it has been. How many different paths can the ant take to the most distant corner?

A. 6

B.12

C.18

D.24

E.30

Make the cube and select two opposite corners. One where the ant is right now and the second is where it wants to reach.

Notice that from its current position, it has 3 different paths that it can take i.e. it has 3 possible options. Make the ant move on any one path out of these 3.

Once one path is chosen, it has two different paths it can take (it cannot take the third one since it cannot revisit the third point). Make the ant move on any one path out of these 2.

Now, from this point, it again has 3 options to reach the point where it wanted to reach. Notice that the case will be the same even if you had selected different paths in the first two moves because it is a cube so all sides are the same.

Total number of different paths = 3*2*3 = 18

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Karishma

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