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#1 marumaru

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Posted 30 December 2007 - 10:03 AM

my friends at school shared these 'puzzles' during our break to avoid boredom. I dunno where they got them so I also don't know if some of these are already posted in this site.

ESCAPE of MARTHA
A wicked wizard banished Martha to a room and the only exits available are two doors (no windows, no chimneys, no exit except those two doors). One door leads to her freedom, another leads to her doom; However, she doesn't know which is which. In the middle of the room are two goblins. One always tell the truth and the other always lie, and again, Martha doesn't know which goblin tells the truth or which goblin lies. What question must she ask in order to know which of the two doors is the door to freedom if she is only permitted to ask ONE question? The question may be asked from one goblin or both or them, as log as it is only a SINGLE question. If she exceeds one question, she will be imprisoned forever. Let us suppose that the goblins are fairly intelligent and they do not side on anyone. (I don't know why the wizard is so mad at Martha but that is not our problem. Good Luck Martha! :)
THE WATER PROBLEM
You are a prisoner in King Noia's contest. There are two glasses of water, and a big pail. To save yourself, you must solve this problem. How would you place the water in the big pail, if the requirements are:
1. you must know which water came from which glass
2. you are not allowed to use any sort of divider
3. only PURE water must be present in the pail

LOCKED with LOCKERS
In a school with 1000 OPENED lockers arranged in a ordered and single line, a teacher made an experiment with 1000 of her students. She calls the first student and asked him to go to all lockers which are multiple of one and close the lockers which are opened OR open the lockers which are closed. She then calls the 2nd student and asked her to go to the lockers which are located at multiples of two and do the same thing. In short, a student goes to the ALL lockers which are MULTIPLE to his/her number and close them if they are opened OR open them if they are closed (example: student #55 goes to all lockers found at locations which are multiple of 55, and closes them if they opened OR opens them if they are closed). Which lockers are opened and which lockers are closed at the end of this so-called 'experiment'?
(Let us suppose that all students have infinite stamina to survive the long process)
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#2 rookie1ja

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Posted 30 December 2007 - 11:25 AM

I dunno where they got them so I also don't know if some of these are already posted in this site.


only ESCAPE of MARTHA is on this site - check Honestants and Swindlecants III.
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#3 bonanova

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Posted 30 December 2007 - 12:55 PM

ESCAPE of MARTHA
Spoiler for solution
THE WATER PROBLEM --
Spoiler for solution
LOCKED with LOCKERS
Spoiler for solution

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 PDR

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Posted 14 January 2008 - 12:33 AM

regarding Bonova's solutions:
Spoiler for The Water Problem
Spoiler for LOCKED with LOCKERS

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#5 bonanova

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Posted 14 January 2008 - 07:32 AM

Spoiler for The reason is ...

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 oranfry

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Posted 14 January 2008 - 10:16 PM

LOCKED with LOCKERS

Thanks bonanova, I agree. If I may throw my own explanation into the ring (as an alternative, not to compete with yours!).

First, understand that this problem is equivalent to:
There are 1000 open lockers numbered 1 to 1000. For each number from 1 to 1000 you take that many stones and try to arrange them into rectangles (squares included of course). For every rectangle you can make of unique width and height, change the state of the corresponding locker.

Spoiler for Continued...

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