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Logic Problems


Zastrugus

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I have alway loved Logic problems....Things that cannot be solved with a computer or calculator. Things that make you THINK....
Below I will post 2 of the Best Logic problems....
Please, let's have some feedback as to how all of you feel about this....
These problems require some extended thought....

Now the questions....

1) You are in a room. There are 2 doors, one at either end.
You are told that one door leads to Freedom and the other door leads to Instant Death.
In addition, there is a guard outside of each door. One guard is a TruthTeller (everything that he says is the absolute truth. The other guard is a Liar (Everything that comes out of his mouth is a lie).
You don’t know which door is which OR which guard is behind which door (don’t automatically assume that the Liar is behind the Death door).

You are allowed to ask ONE question of either guard and use that information to get out safely EVERY time.

Two part question ---- What is the question and how does the information get you out safely?

2) Knight Moves
This question requires that you know how a Knight moves on a chess board.
Is possible (must give a reason as to why it is or is not possible), to start a Knight in one corner of a chess board, touch each square once and only once and end up on your last move on the diagonally opposite square.

DO NOT ATTEMPT TO MAKE THE MOVES….Simply give a logical reason as to why it is or is not possible….Guesses without explanation will be ignored....

I will post the answers within a week....

 

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Solution for logic puzzle 1 :

Question  "If I asked what door would lead to freedom, what door would the other guard point to ?"

If I asked the truth-guard, the truth-guard would tell me that the liar-guard would point to the door that leads to death.

If I asked the liar-guard, the liar-guard would tell me that the truth-guard would point to the door that leads to death.

Therefore, no matter who you ask, the guards tell you which door leads to death, and therefore you can pick the other door.

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You could also ask a more simple question, one which you already know the answer to is absolute truth. E.g. "Does 1 plus 1 equal 3?" Liar would say yes, truther would say no.

 

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Sorry Bluescope....While that may identify the Truthteller from the Liar....That doesn't get you the information needed to escape....

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Well, without using Google, why not simplify the question to the square circle plus which door leads to death? You know the liar will say yes to the first and lie about the second, the Truther will say no to the first and point to the door of death.

 

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Since there were no further replies, I will post the answers....

 

1)  What door would the other guard tell me to use to get out safely....And then do the opposite....

If you asked the truth-guard, the truth-guard would tell you that the liar-guard would point to the door that leads to death.

If you asked the liar-guard, the liar-guard would tell you that the truth-guard would point to the door that leads to death.

Therefore, no matter who you ask, the guards tell you which door leads to death, and therefore you can pick the other door.


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2) Knight Moves

A chess board has 64 squares (8x8)….The diagonally opposite squares are the same color….A Knight moves 2 squares up or down and 1 square right or left….

When a knight moves it always lands on a different color from where it started….

 

So, if a knight starts in one corner, there are 63 other squares, so on the 63rd move (an odd number) it is impossible to land on the same color that you started with….

 

 

 

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