Aptitude Discussion

Q. |
$PQRSTU$ is a regular hexagon drawn on the ground. Prashant stands at $P$ and he starts jumping from vertex to vertex beginning from $P$. From any vertex of the hexagon except $S$, which is opposite to $A$, he may jump to any adjacent vertices. When he reaches $S$, he stops. Let Sn be the number of distinct paths of exactly $n$ jumps ending at $S$. What is the value of $S^2k$, where $k$ is an integer? |

✔ A. |
$0$ |

✖ B. |
$4$ |

✖ C. |
$2k$ |

✖ D. |
Depends on the value of $k$ |

**Solution:**

Option(**A**) is correct

The least number of jumps required to reach $S$ without any backtracking is 3.

Every time there is back tracking, there is an increase of two jumps.

Hence the number of jumps is always odd.

Whenever the number of jumps is even, there is no paths to reach $S$.

Since '$2k$' is even $S^2k=0$

**Shikhar**

*()
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i didnt get the explaination