Puzzle for Halflife2.net

[Acepilotf14]

You didn't, really? The boat flipped over for a good reason.

Explain.

 

[ericms]

They didn't get "wet" because they were married and not single. It's a sexual innuendo.

 

[Jintor]

I love these forums.

 

[Crushenator 500]

They didn't get "wet" because they were married and not single. It's a sexual innuendo.

Actually I'm pretty sure the wet part is irrellevant, it's just saying that there werent any single men on the boat, so when it says "not a single man got wet", it doesn't mean they didn't get wet, it means that they all had partners. It's an english puzzle, not a sexual one

The whole boat got wet, not a single man

 

[Acepilotf14]

They didn't get "wet" because they were married and not single. It's a sexual innuendo.

Yes, but where does the orgasm come from? I don't see how a boat tipping over can cause sexual stimulus.

 

[ericms]

Actually I'm pretty sure the wet part is irrellevant, it's just saying that there werent any single men on the boat, so when it says "not a single man got wet", it doesn't mean they didn't get wet, it means that they all had partners. It's an english puzzle, not a sexual one

The whole boat got wet, not a single man

I'm sorry, I thought I remembered it being a couple that was on the boat. I actually thought of a pretty good spin-off of that one then. My thought process was that since they were an old married couple she wasn't aroused.

Yes, but where does the orgasm come from? I don't see how a boat tipping over can cause sexual stimulus.

I was thinking the other way around.

 

[Dan]

Ok, I guess the police inspector problem was too hard. If you want a hint on how it is done, a guy named Richard Hamming solved the fundamental problem over a half century ago. Here is another problem:

You are one of three prisoners who have been sentenced to death by a sadistic warden. The warden plays this game with you where if you win you get your freedom, if you lose, you die. He has a bag with 3 black hats and 2 white hats inside. While blindfolded, each of you reach into the bag and choose one to place on your head. The blindfolds are removed, and you see that the other two prisoners have a black hat, but you can't see your own hat. All three of you must then remain in the room until you guess what colour hat you have one, but you can't communicate otherwise. An important fact, is that you know that you are more clever than the other two prisoners, and if there is something to be figured out, you will figure it out first. After a while, you tell the warden what colour hat you have on and you walk free. What colour was it?

If you find that one too easy or get bored, here is another one which actually combines elements from the previous two puzzles (both still unsolved, come on guys!):

There is a gameshow similar to the warden's game. The way it works is this: There are three players. Each player is randomly assigned a black or white hat. The players get to see each others hat, but not their own. The players may not communicate, except for a strategy planning session before the game. All three players must then simultaneously either declare the colour of their hat or say that they pass. If atleast one player guesses correctly, and no players guess incorrectly, the entire team wins 3 million dollars. But if one or more players guess wrong, or everybody passes, then the whole team loses. What is the optimal strategy for this game, and what winning percentage can be achieved?

 

[ericms]

You are one of three prisoners who have been sentenced to death by a sadistic warden. The warden plays this game with you where if you win you get your freedom, if you lose, you die. He has a bag with 3 black hats and 2 white hats inside. While blindfolded, each of you reach into the bag and choose one to place on your head. The blindfolds are removed, and you see that the other two prisoners have a black hat, but you can't see your own hat. All three of you must then remain in the room until you guess what colour hat you have one, but you can't communicate otherwise. An important fact, is that you know that you are more clever than the other two prisoners, and if there is something to be figured out, you will figure it out first. After a while, you tell the warden what colour hat you have on and you walk free. What colour was it?

Sorry, by clever do you mean he seemingly has more information than the others or that he is inherently more clever than them?

 

[Dan]

Sorry, by clever do you mean he seemingly has more information than the others or that he is inherently more clever than them?

you are smarter than they are

 

[ericms]

So if your hat was white then one of the other prisoners would see both a white and black hat. That prisoner would know his hat couldn't be white otherwise the last prisoner would see two white hats and know his was black. If that were not the case then the first prisoner considered would know his was black. So your hat must be black and since you're under the same condition as the other two but more clever you win.

Dan, you love this style of puzzle too much. The ones where you must exhaust every case. I hate you for it.

 

[Gormanmod]

I still don't understand this thread at all.

 

[Pesmerga]

I still don't understand this thread at all.

Maybe that's because you're ****ing stupid.

 

[Gormanmod]

or maybe it's because I'm quarantined in the hospital with MRSA being pumped with mind-altering drugs? LOL/

 

[ericms]

I still don't understand this thread at all.

****, I thought you were W4d5Y. There goes a good joke.

 

[Gormanmod]

How does I put on tin hatz?

 

[ericms]

Dan, I'll try the second one in a little while. Feel free to post more if you want.

Easier:

All of those registered at "Halflife2.net" are either mods or members. Mods always tell the truth and members always lie. A person says "I am a liar." Show that he doesn't have a registered account at "Halflife2.net."

Harder:

In how many ways can one travel from the point (0,0) to (5,5) while only moving up and to the right and only on adjacent points with integer values?

Try not to brute force the last one. Maybe use simpler cases to find a way of thinking.

 

[Crushenator 500]

All of those registered at "Halflife2.net" are either mods or members. Mods always tell the truth and members always lie. A person says "I am a liar." Show that he doesn't have a registered account at "Halflife2.net."

They can't be a member because they would be lying about lying, which means they would be telling the truth, but then they can't be a mod because mods aren't liars.

 

[ericms]

They can't be a member because they would be lying about lying, which means they would be telling the truth, but then they can't be a mod because mods aren't liars.

Weren't you a truth-teller once? Heh, good job though.

 

[Acepilotf14]

All the members of hl2.net are stupid. Explain how one could have an average IQ of 137.

 

[Dan]

All the members of hl2.net are stupid. Explain how one could have an average IQ of 137.

One person doesn't have an average IQ, just an IQ. Also, the internet IQ sites all lie to get you to pay money to them.

 

[Dan]

Harder:

In how many ways can one travel from the point (0,0) to (5,5) while only moving up and to the right and only on adjacent points with integer values?

Try not to brute force the last one. Maybe use simpler cases to find a way of thinking.

Seems like a simple case of Pascal's triangle. I will go with the answer being 10 choose 5, which equals 252. I just punched it into a calculator, but if you wanted to do it by hand, it would be 10!/(5!(10-5)!)

For latecomers, I will repost the 2 still unsolved problems I have put up:

There is a game show similar to the warden's game. The way it works is this: There are three players. Each player is randomly assigned a black or white hat. The players get to see each others hat, but not their own. The players may not communicate, except for a strategy planning session before the game. All three players must then simultaneously either declare the colour of their hat or say that they pass. If atleast one player guesses correctly, and no players guess incorrectly, the entire team wins 3 million dollars. But if one or more players guess wrong, or everybody passes, then the whole team loses. What is the optimal strategy for this game, and what winning percentage can be achieved? Here's a hint, it's greater than 50%


An evil genius kidnaps the princess of Moldova. He sends a letter to the police chief saying that he will execute the princess unless the chief can guess a specific number between 1 and 2000 which the evil genius is thinking of. He explains further that the chief can post in the newspaper an ad containing up to 15 yes or no questions about the number he is thinking of, and he will send a reply with his answers. But the catch is that he may or may not lie about one of the answers. What 15 questions can the police chief ask to ascertain the exact number the evil genius is thinking of and get the princess returned safely? If you really have no idea where to start, I gave the hint that the work of Richard Hamming would be helpful for solving this problem. Don't worry it's not overly complicated mathematics.

 

[ericms]

Right, since you have 5 x-moves and 5 y-moves in any combination you can consider it as all the different combinations of that 10 element string which is just as you said.

 

[Druckles]

In how many ways can one travel from the point (0,0) to (5,5) while only moving up and to the right and only on adjacent points with integer values?

70?

I thought the answer would be in pure maths with a few 4!, 5! or something similar, and I couldn't be bothered. So I started to count up. Trying to make it simpler and keep count, I jotted the numbers down the side. I realised it was getting to complicated, and I was losing count, so I redrew it...

If the answer's right, I'll tell you how I got it

 

[Dan]

70?

I thought the answer would be in pure maths with a few 4!, 5! or something similar, and I couldn't be bothered. So I started to count up. Trying to make it simpler and keep count, I jotted the numbers down the side. I realised it was getting to complicated, and I was losing count, so I redrew it...

If the answer's right, I'll tell you how I got it

It was 252, see above

 

[Druckles]

Edit: Heh, I worked it out for a 4x4 grid. Yeah, a 5x5 would be 252

 

[Dan]

I stick with 70. You didn't prove it, you simply stated the answer.

I did prove it, if you look up a few posts. It's Pascal's triangle. Each street is a binary decision, up or right. Look it up on wikipedia and you will see that the 5th entry on the 10th line is 252. Pascals triangle can be calculated for any coordinate using nCr. I just punched 10 nCr 5 on my calculator to get the answer. I also showed you how to manually calculate the solution.

 

[Druckles]

You said "It's Pascals triangle". Doesn't explain much. But I've already said you're right.

And as for the hat problem. If someone sees the other two people have different colour hats, they pass, if someone sees the other two people have the same colour hat, then they say a different colour to that which they see. This would work in all cases but two, in which the hats are all the same colour, and everyone would call out the opposite colour. The success rate is 75%.

 

[ericms]

There are 3x3 dots on a piece of paper that are evenly spaced in each of four directions (above, below, left, and right). Can you draw just three lines without lifting your pencil such that they cover every dot?

. . .
. . .
. . .

Sort of like that. Yes, I meant three lines and not four.

 

[Druckles]

Um... the only combinations I see leave two dots left over. And the only solution I can come up with is that if you drew infinitely long lines, you could go up, then down and then up again... and have three parallel lines...

 

[ericms]

Actually, you can solve it in only one.

 

[Druckles]

Solve it with one line...? Now that's impossible. Unless it's a trick questions.

 

[Dan]

He didn't say they had to be straight lines, although mathematically a line has to be perfectly straight. But mathematically, the infinite line solution also works.

 

[ericms]

This is probably too revealing of a hint, but keep to the paper and pencil analogy of the question.

 

[Druckles]

I figured they would be, otherwise why ask for three? A curved line essentially employs an infinite number of straight lines... so why bother asking for any number of lines if you're just going to accept a curved line.

 

[ericms]

I'm not. That's what Dan said, not me. This isn't a mathematically rigorous question.

The reason I originally said three was because earlier this morning I solved one where you could use four, but with only three.

Edit: By the way, that means the problem is still unsolved.

 

[Dan]

The four line problem goes back to job interviews in the 80s and coined the term thinking outside of the box. For fewer lines, you could fold the paper and put the dots into a line.

 

[ericms]

Yeah, basically what I was looking for. Dan, if you don't mind me asking, what field of work are you in? Or are you still in school?

 

[Dan]

finishing a mechanical engineering degree this spring

 

[Dan]

Here's a simple problem from the Microsoft interview process: Why are manhole covers round?

Here's a harder problem:

Take a look at the two paths in the picture below. They trace out the path of a bicycle (one path for each wheel). The path continue on outside of the picture (so the start and end points of the curves aren't necessarily the start or end of the bicycles journey). Which line goes with the front wheel, and which with the back wheel? Which direction did the bicycle travel? Right to left, or left to right?

And here is one more even harder problem (even if not many people are trying these). Calculus might help but you can solve it without it:

On a certain winter day, snow starts to fall at a heavy and steady rate. Three identical snowplows start plowing the same road, the first leaving at 12 noon, the second leaving at 1 pm, and the third leaving at 2 pm. At some time later, they all collide. At what time did the snow start to fall? Edit: after further review, I can't see how to solve this without using differential equations, or some heavy duty numerical methods.

Note: Assume that the speed of a snowplow is inversely proportional to the depth of the snow.

There is still the problem of the princess of Moldova left to solve as well:

An evil genius kidnaps the princess of Moldova. He sends a letter to the police chief saying that he will execute the princess unless the chief can guess a specific number between 1 and 2000 which the evil genius is thinking of. He explains further that the chief can post in the newspaper an ad containing up to 15 yes or no questions about the number he is thinking of, and he will send a reply with his answers. But the catch is that he may or may not lie about one of the answers. What 15 questions can the police chief ask to ascertain the exact number the evil genius is thinking of and get the princess returned safely? If you really have no idea where to start, I gave the hint that the work of Richard Hamming would be helpful for solving this problem. Don't worry it's not about advanced mathematics or anything.

Here are some for those of you who are less mathematical, but still want to pretend to be smart :
The first 25 letters of the alphabet are written out so that it is in two lines. The top line contains the letters B, C, D, G, J, O, P, Q, R, S, U. The bottom line contains the letters A, E, F, H, I, K, L, M, N, T, V, W, X, Y. Where would Z go?

next one:

Only one of the following multiple choice answers is correct. Which is it?
A) Answer A
B) Answer A, and B
C) Answer B, and C


...and last one for today:

A stupid thief steals the car on the police chief without realizing who it belongs to. The police have 4 suspects that they bring in and question using a new lie detector. These are their statements:

Suspect A:

1. In high-school I was in the same class as suspect C.
2. Suspect B has no driving license.
3. The thief didn't know that it was the car of the chief of police.

Suspect B:

1. Suspect C is the guilty one.
2. Suspect A is not guilty.
3. I never sat behind the wheel of a car.

Suspect C:

1. I never met suspect A until today.
2. Suspect B is innocent.
3. Suspect D is the guilty one.

Suspect D:

1. Suspect C is innocent.
2. I didn't do it.
3. Suspect A is the guilty one.

The lie detector isn't very good though because it only tells them that four out of the twelve statements were true and not which ones. Who is the thief?

Okay, one more:

Two friends, Omar and Xavier, are playing tic-tac-toe, but they strictly follow two rules during the game. The first rule is that if you can win on your turn, you must win. The second rule if your opponent is about to win on the next turn, you must try to prevent it, unless the first rule applies.

We don't know who went first, but this is what the game looks like:

O|O|_
O|X|_
X|X|

Who will win?

 

[Dan]

Since I put a lot of effort into adding many new puzzles, I thought I would bump this up for others to see and try.