# Thread: Word problems for fun!

1. Hooray for feelers solving riddles!

2. Three Masters of Logic wanted to find out who was the wisest amongst 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?

3. Let us name the men A, B, and C respectively; furthermore, let us assume that A is the man who guessed correctly.

A observes that both B and C have raised their hands, indicating both have seen a red dot. However, let us assume that A is observed to have a blue dot on his head. Then, when B saw C raising his hand, he must conclude that he, B, has a red dot, since C could only see a red dot on his forehead. Therefore, he would have immediately guessed that his dot was red. Therefore, since A having blue would immediately lead to a correct guess by either B or C, he must have a red dot.

This solution assumes that the man who guessed correctly believes the other men to be smart enough to guess rather quickly should he have had a blue dot. This, of course, isn't a certainty. I would imagine if the other two had down syndrome, or some other mental defect, he would have had a more difficult time.

Edit: The essential part of this problem rests in the fact that if at least one blue dot is present, then guesses will come within a given time X. A person must be certain of the fact that the others haven't been able to reach a conclusion before he himself can make one. Without this, it cannot be known with certainty.

4. Originally Posted by Jonnyboy
Let us name the men A, B, and C respectively; furthermore, let us assume that A is the man who guessed correctly.

A observes that both B and C have raised their hands, indicating both have seen a red dot. However, let us assume that A is observed to have a blue dot on his head. Then, when B saw C raising his hand, he must conclude that he, B, has a red dot, since C could only see a red dot on his forehead. Therefore, he would have immediately guessed that his dot was red. Therefore, since A having blue would immediately lead to a correct guess by either B or C, he must have a red dot.

This solution assumes that the man who guessed correctly believes the other men to be smart enough to guess rather quickly should he have had a blue dot. This, of course, isn't a certainty. I would imagine if the other two had down syndrome, or some other mental defect, he would have had a more difficult time.

Edit: The essential part of this problem rests in the fact that if at least one blue dot is present, then guesses will come within a given time X. A person must be certain of the fact that the others haven't been able to reach a conclusion before he himself can make one. Without this, it cannot be known with certainty.
That is an interesting angle, psychologically speaking. Your analysis is of course correct, but my personal approach was: if A had a blue dot, this would give the other two men an unfair advantage over him because for him his dot could technically be either color (provided nobody lied) while the other two would have been able to almost immediately see that theirs had to be red.

Be it because we assume the others aren't stupid or because we assume the chances of winning the challenge have to be even, we path there is the same. So we agree.

5. Suppose there exist 1000 gold coins which are to be split up among ﬁve pirates: 1,2,3,4, and 5 in order of rank. We assume that the coins must remain wholly intact and that the pirates have the following characteristics: a pirate is inﬁnitely knowledgeable; a pirate values his own life above wealth and above his need to kill, and will thus always vote for his own proposal; a pirate will always choose a greater amount of wealth over killing another pirate; caeteris paribus, a pirate will kill another pirate if given the chance; a pirate is risk neutral.

Starting with the highest numbered pirate, he can make a proposal as to how the coins will be split up. This proposal can either be accepted or the pirate making the proposal is killed. A proposal is accepted if and only if a majority of the pirates accept it. If a proposal is accepted the coins are split up in accordance with the proposal. If a proposal is rejected and the pirate making the proposal is killed, the next ranking pirate makes a proposal, so on and so forth.

What proposal should pirate 5 make?

6. A man has a lighter and two lengths of robe with varying densities. The only thing the man knows about each length of rope is that if he lights an end of a rope, it will burn for exactly one hour; however, it may be that 90% of a rope burns up in 1 minute, and it takes 59 minutes for the remaining section of rope to burn (this is a product of the varying densities).

How can this man accurately measure 45 minutes?

7. I see a thing. Of this thing I know these three:
1) The man who makes this will sell it.
2) The man who buys this will not use it.
3) The man who uses this will not know it.

What do I see?

8. Ever heard of vampires?

9. Originally Posted by Red Herring
Ever heard of vampires?

10. Originally Posted by Jonnyboy

What proposal should pirate 5 make?
He should offer one coin each to 1 & 3 and offer nothing to the others.

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