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## Tuesday, July 29, 2008

### The Masters Plaza

Thanks to Hassan Issa from Lebanon, we can present you the following puzzle:

You have the chance to take your room in the "Masters Plaza", a hotel in which 5 masters (5 of the most intelligent people who ever lived) are present. The hotel consists of 5 rooms and a small restaurant that contains 5 tables. Each master has a rank which shows his level of thinking with respect to the whole group. The master with the first rank is said to be the head master, and he is not you. Rooms, as well as tables, are successively numbered from 1 to 5 in a way that each master lives in a room and eats on a table different in number from his rank. To avoid confrontation, masters with successive ranks are neither allowed to live in rooms next to each other nor to eat on tables next to each other. The four present masters are: Albert Einstein, Galileo Galilei, Hassan Issa and Archimedes. To have your room in the Plaza, you just have to know your rank, table number and room number knowing that:

* Archimedes doesn't eat on the fifth table.
* Einstein is not the head master.
* Archimedes has exactly the middle rank between Hassan and You.
* Einstein is more intelligent than Archimedes.
* Galileo eats on a table next to that of Einstein.
* Hassan does not eat on a table with the same number as his room number.

The Question: What are the ranks, room numbers, and table numbers of the five masters?

Answer: The first step is to know the ranks of the 5 masters.

Archimedes has a middle rank between Hassan and You. Then Archimedes has the 2nd, 3rd or 4th rank.

If Archimedes is in the 2nd rank then Hassan has the first and You have the 3rd rank. So Einstein can't have a higher rank than Archimedes, so this possibility is false.

If Archimedes has the 4th rank then Hassan and You are in the 3rd and 5th rank, so Galileo and Einstein have the 1st and the 2nd rank which is impossible because they eat on tables next to each other.

If Archimedes has the 3rd rank and Hassan and You have the 2nd and the 4th rank then Einstein has the 1st rank and Galileo has the 5th, because Einstein is more intelligent than Archimedes, and that is impossible because Einstein is not the head master.

The only true possibility is that Archimedes has the 3rd rank, Hassan has the 1st and You the 5th, because You are not the headmaster. Then Einstein has the 2nd rank and Galileo the 4th, because Einstein is more intelligent than Archimedes.

The second step is to list all the possibilities for successive ranks so that they are not next to each other.

Here two possibilities are true as shown in the table but Archimedes (rank 3) doesn't eat on the 5th table, so the 1st possibility is not the table number. The 2nd possibility is true in table and room numbers case, but since Hassan does not eat on a table with the same number as his room number, then the 2nd possibility is for the table number and the 1st for the room number. The results are shown in this table:

Copyright © 2005 by Hassan Issa, Lebanon. Published on this website with permission.