# Seating Arrangement

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There are 8 houses in a line and in each house only one boy lives with the conditions as given below:

1. Jack is not the neighbour of Siman.
2. Harry is just next to the left of Larry.
3. There is at least one to the left of Larry.
4. Paul lives in one of the two houses in the middle.
5. Mike lives in between Paul and Larry.

If at least one lives to the right of Robert and Harry is not between Taud and Larry, then which one of the following statement is not correct?

1. Robert is not at the left end.
2. Robert is in between Simon and Taud.
3. Taud is in between Paul and Jack.
4. There are three persons to the right of Paul.

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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.

1. Robert is not at the left end. – Possible as shown
2. 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.

1. Robert is not at the left end. – Possible as shown in first case
2. Robert is in between Simon and Taud. – Possible as shown in first case
3. Taud is in between Paul and Jack. – Possible as shown in second case
4. There are three persons to the right of Paul. – Possible as shown in second case
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