Interpreting the given statements as follows
- Harry is just next to the left of Larry.
- There is at least one MORE to the left of Larry. (otherwise this is trivial from the above statement)
It is given that $P$ lives in one of the middle houses. Lets assume it is the fourth position.
$\begin{array}{|c|c|c|c|c|c|c|c|}\hline&&&P&&&&\hline\end{array}$
$H \;L$ should come together.
There is at least one more to the left of Larry.
So, if $H\;L$ comes to the left of $P,$ then the three positions to left of $P$ are filled with $L$ being the immediate neighbour of $P$ which is not possible as it is given that “Mike lives in between Paul and Larry.” So, $H\;L$ should be to the right of $P.$
and the possibilities are $\begin{array}{|c|c|c|c|c|c|c|c|}\hline&&&P&M&&H&L\\ \hline\end{array}$ or $\begin{array}{|c|c|c|c|c|c|c|c|}\hline&&&P&M&H&L&\\ \hline\end{array}$ or $\begin{array}{|c|c|c|c|c|c|c|c|}\hline&&&P&&M&H&L\\ \hline\end{array}$
Harry is not between Taud and Larry
Since $H\;L$ is together this means $T$ is to the right of $L.$ Thus from the $3$ possibilities $2$ are eliminated and we get $\begin{array}{|c|c|c|c|c|c|c|c|}\hline&&&P&M&H&L&T\\ \hline\end{array}$
Jack is not the neighbour of Siman
This means $R$ should come in between them $\begin{array}{|c|c|c|c|c|c|c|c|}\hline(J|S)&R&(J|S)&P&M&H&L&T\\ \hline\end{array}.$ All the given conditions are satisfied here.
Now, lets see the options.
- Robert is not at the left end. – Possible as shown
- Robert is in between Simon and Taud. – Possible if $S$ comes to the extreme left.
Now lets take the other possibility of $P$ taking the fifth position.
$\begin{array}{|c|c|c|c|c|c|c|c|}\hline&&&&P&&&\hline\end{array}$
Now $H\;L$ cannot be on the RHS of $P$ as $M$ should be between $P$ and $L$ and $T$ should be to the right of $L$ meaning we need $4$ places to the right of $P$ but we have only $3.$ So, $H\;L$ should be to the left of $P$ and we get
$\begin{array}{|c|c|c|c|c|c|c|c|}\hline R&H&L&M&P&(J|S)&T&(J|S)\\\hline\end{array}$
Now, lets see the options.
- Robert is not at the left end. – Possible as shown in first case
- Robert is in between Simon and Taud. – Possible as shown in first case
- Taud is in between Paul and Jack. – Possible as shown in second case
- There are three persons to the right of Paul. – Possible as shown in second case