the problem

Problem

1. In a certain mythical community, politicians never tell the truth, and nonpoliticians always tell the truth. A stranger meets three natives and asks the first of them, “ Are you a politician?”. The first native answers the question. The second native then reports that the first native denied being a politician. The third native says that the first native is a politician. How many of these three natives are politicians?

2. On a certain train, the crew consists of the brakeman, the fireman, and the engineer. Their names listed alphabetically are Jones, Robinson and Smith. On the train are also three passengers with corresponding names, Mr. Jones, Mr. Robinson, and Mr. Smith. The following facts are known:
a. Mr. Robinison lives in Detroit
b. The brakeman lives exactly halfway between Detroit and Chicago
c. Mr. Jones earns exactly $20,000 a year
d. Smith oncea beat the fireman at the billiards
e. The brakeman’s next door neighbor, one of the three passengers mentioned, earns exactly three times as much as the brakeman
f. The passenger living in Chicago has the same name as the brakeman.

What is the engineer’s name?

3.The Waiter
Three men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognizes the three as friends and asks the waiter to return $5 to the men.
The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.
Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14.....where has the other $1 gone from the original $15?



4. The Double Jeopardy Doors
You are trapped in a room with two doors. One leads to certain death and the other leads to freedom. You don't know which is which.
There are two robots guarding the doors. They will let you choose one door but upon doing so you must go through it.
You can, however, ask one robot one question. The problem is one robot always tells the truth ,the other always lies and you don't know which is which.
What is the question you ask?

due next meeting...
explain on how you solve the problem
no copying