Competition problem — Combinatorics

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Combinatorics Difficulty 1.6 Junior Find the answer

Lian, Marzuq, Rafsan, Arabi, Nabeel, and Rahul were in a 12-person race with 6 other people. Nabeel finished 6 places ahead of Marzuq. Arabi finished 1 place behind Rafsan. Lian finished 2 places behind Marzuq. Rafsan finished 2 places behind Rahul. Rahul finished 1 place behind Nabeel. Arabi finished in 6th place. Who finished in 8th place?
$\textbf{(A)}\; \text{Lian}$ $\textbf{(B)}\; \text{Marzuq}$ $\textbf{(C)}\; \text{Rafsan}$ $\textbf{(D)}\; \text{Nabeel}$ $\textbf{(E)}\; \text{Rahul}$

Your answer

Multiple choice: answer with the letter of the option you want.

Solution

Let --- denote any of the 6 racers not named. Then the correct order looks like this:
$-, \text{Nabeel}, \text{Rahul}, -, \text{Rafsan}, \text{Arabi}, -, \text{Marzuq}, -, \text{Lian}, -, -$
Thus the 8th place runner is $\boxed{\textbf{(B)}\; \text{Marzuq}}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.