LOGIC PUZZLE: MASTERS OF LOGIC PUZZLES - STAMPS

MASTERS OF LOGIC PUZZLES - STAMPS

The Grand Master takes a set of 8 stamps, 4 red and 4 green, known to the logicians, and loosely affixes two to the forehead of each logician. so that each logician can see all the other stamps except those 2 in the Grand Master's pocket and the two on her own forehead.

He asks them in turn if they know the colors of their own stamps:

       A: "No"

       B: "No"

       C: "No"

       A: "No"

       B: "Yes"

          What color stamps does B have?

Solution:

B says: 

"Suppose I have red-red. A would have said on her second turn: 'I see that B has red-red. If I also have red-red, then all four reds would be used, and C would have realized that she had green-green. But C didn't, so I don't have red-red. Suppose I have green-green. In that case, C would have realized that if she had red-red, I would have seen four reds and I would have answered that I had green-green on my first turn. On the other hand, if she also has green-green (we assume that A can see C; this line is only for completeness), then B would have seen four greens and she would have answered that she had two reds. So C would have realized that, if I have green-green and B has red-red, and if neither of us answered on our first turn, then she must have green-red."

'But she didn't. So I can't have green-green either, and if I can't have green-green or red-red, then I must have green-red.'

So,B continues:

"But she (A) didn't say that she had green-red, so the supposition that I have red-red must be wrong. And as my logic applies to green-green as well, then I must have green-red."


So, B had green-red, and we don't know the distribution of the others certainly.

(Actually, it is possible to take the last step first, and deduce that the person who answered YES must have a solution which would work if the greens and reds were switched -- red-green)

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LOGIC PUZZLE: MASTERS OF LOGIC PUZZLES - HATS

After losing the "Spot on the Forehead" contest, the two defeated Puzzle Masters complained that the winner had made a slight pause before raising his hand, thus derailing their deductive reasoning train of thought. And so the Grand Master vowed to set up a truly fair test to reveal the best logician among them.

He showed the three men 5 hats - two white and three black.

Then he turned off the lights in the room and put a hat on each Puzzle Master's head.

After that the old sage hid the remaining two hats, but before he could turn the lights on, one of the Masters, as chance would have it, the winner of the previous contest, announced the color of his hat.

And he was right once again.

What color was his hat?

What could have been his reasoning?

Solution:

The important thing in this riddle is that all masters had equal chances to win.

If one of them had been given a black hat and the other white hats, the one with black hat would immediately have known his color (unlike the others). 

So, 1 black and 2 white hats are not a fair distribution.

If there had been one white and two black hats distributed, then the two with black hats would have had advantage.

They would have been able to see one black and one white hat and supposing they had been given white hat, then the one with black hat must at once react as in the previous situation.

However, if he had remained silent, then the guys with black hats would have known that they wear black hats, whereas the one with white hat would have been forced to eternal thinking with no clear answer. So neither this is a fair situation.

That's why the only way of giving each master an equal chance is to distribute hats of one color - so 3 black hats.

I hope this is clear enough.

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LOGIC PUZZLE: MASTERS OF LOGIC PUZZLES - DOTS 

Masters of Logic wanted to find out who was the wisest among them. So they turned to their Grand Master, asking to resolve their dispute.

"Easy," the old sage said. "I will blindfold you and paint either red, or blue dot on each man's forehead. When I take your blindfolds off, if you see at least one red dot, raise your hand. The one, who guesses the color of the dot on his forehead first, wins."

And so it was said, and so it was done. The Grand Master blindfolded the three contestants and painted red dots on every one. When he took their blindfolds off, all three men raised their hands as the rules required, and sat in silence pondering. Finally, one of them said: "I have a red dot on my forehead."

How did he guess?






Solution:

The wisest one must have thought like this:

I see all hands up and 2 red dots, so I can have either a blue or a red dot. If I had a blue one, the other 2 guys would see all hands up and one red and one blue dot. So they would have to think that if the second one of them (the other with red dot) sees the same blue dot, then he must see a red dot on the first one with red dot. However, they were both silent (and they are wise), so I have a red dot on my forehead.

Here is another way to explain it:

All three of us (A, B, and C (me)) see everyone's hand up, which means that everyone can see at least one red dot on someone's head. If C has a blue dot on his head then both A and B see three hands up, one red dot (the only way they can raise their hands), and one blue dot (on C's, my, head). Therefore, A and B would both think this way: if the other guys' hands are up, and I see one blue dot and one red dot, then the guy with the red dot must raise his hand because he sees a red dot somewhere, and that can only mean that he sees it on my head, which would mean that I have a red dot on my head. But neither A nor B say anything, which means that they cannot be so sure, as they would be if they saw a blue dot on my head. If they do not see a blue dot on my head, then they see a red dot. So I have a red dot on my forehead.

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LOGIC PUZZLE : BULB                                                

BULBS

There are three switches downstairs.

Each corresponds to one of the three light bulbs in the attic. 

You can turn the switches on and off and leave them in any position.

How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?

SOLUTION:

Keep the first bulb switched on for a few minutes. It gets warm, right?

So all you have to do then is ... switch it off, switch another one on, walk into the room with bulbs, touch them and tell which one was switched on as the first one (the warm one) and the others can be easily identified.

RIVER CROSSING PUZZLE - 3

SHE-GOAT, WOLF AND CABBAGE

A farmer returns from the market, where he bought a she-goat, a cabbage and a wolf (what a crazy market :-). On the way home he must cross a river. His boat is small and won't fit more than one of his purchases. He cannot leave the she-goat alone with the cabbage (because the she-goat would eat it), nor he can leave the she-goat alone with the wolf (because the she-goat would be eaten).

How can the farmer get everything on the other side in this river crossing puzzle?

Solution:

Take the she-goat to the other side.

Go back, take cabbage, unload it on the other side where you load the she-goat, go back and unload it.

Take the wolf to the other side where you unload it. Go back for the she-goat.

That's it.