Logic Puzzles

[Moeboid ●]

I can't be the only one out there who enjoys logic puzzles.

Some rules and tips for this thread:
1. Answers go in spoilers!!!
2. Do not post the answer if you were already familiar with the puzzle. Give those who don't know the answer chance to figure it out first.
3. If you answer a question, and this answer is confirmed by the person who posted the puzzle, you get to post a puzzle of your choice, or pass on that responsibility to someone of your choosing.
4. Don't copy and paste a puzzle from the internet. Use your own words and change a few details so that no one can Google the answer.
5. Puzzles must contain all information necessary to solve the puzzle. No one should have to request additional information.
6. If the current puzzle's author chooses to post hints, they should also be in spoilers.
7. Feel free to request a hint or a different puzzle if you feel the current puzzle is too hard. The puzzle's author may do either of these things if they wish.
8. A puzzle cannot last longer than 3 days. After that time, a new puzzle can be posted by anyone, and the original puzzle's author should post the answer (in a spoiler, of course) when they get time.
9. If the user who posted the correct answer does not post a new puzzle within 48 hours of their answer being confirmed, a new puzzle can be posted by anyone.

I'll start it off:

Four children were told by their mother that she would give them an ice cream if they were able to solve a puzzle. They agreed and were arranged as shown in the diagram below. The black line represents a barrier that the children cannot see through. Once they were in their positions, their mother told them that she had four hats - two black ones and two white ones - and that each would be given one to wear. Each child would be given an ice cream if one of them could correctly identify the colour of the hat that they were wearing. The children failed the puzzle if any of them looked at their own hat, turned around, or said anything other than the correct answer.

Once they had their hats on, the children stood there quietly contemplating the puzzle before one of them suddenly suddenly realised that they could solve the puzzle. They shouted out the correct answer and all were awarded ice creams. Who was it, and how did they know?


In case it's not clear:
Child A can see the colour of the hats worn by children B and C
Child B can see the colour of the hat worn by child C
Children C and D cannot see the colour of anyone's hat.

Edit: This puzzle was solved correctly by philfredobob

Last edited by Moeboid on Thu Aug 01, 2013 5:56 pm, edited 2 times in total.

[philfredobob ●]

There, i put it in a spoiler tag, Moeboid.

Spoiler:

Child B answered, because he can see that child C has a white hat, and child A hasn't said anything, meaning the two people in front of him must have different coloured hats, meaning the colour of Child Bs hat must be Black ?

that's my guess

Last edited by philfredobob on Mon Jul 22, 2013 6:35 pm, edited 2 times in total.

[Dohva. ●]

This thread is fine so long as the topic remains on these puzzles. Have fun!

[Moeboid ●]

Woohoo! Thanks, Dohva!

And you were 100% correct, philfredobob! I am impressed. You solved that fast. Though, please put your answers in spoilers from now on. Your turn to post a puzzle.

[philfredobob ●]

I'll be honest with you, i don't know any. my brother told me a few years ago, and I've been sitting here trying to remember them, but i can't remember what the answers were.

can i pass on this one?

[Moeboid ●]

You certainly may

[philfredobob ●]

I don't actually have anyone picked out to pass it onto. would you happen to have another one?

anybody who has another one can post, i pass on my turn

[Moeboid ●]

I'll post another hat problem, then:

100 children were given the opportunity to participate in a puzzle where they could win an ice cream if they answered correctly. The children were told in advance what the puzzle would be, and were able to spend some time figuring out a strategy as a group. The children were arranged in a straight line, all facing the same direction, and each given either a black or white hat to wear. Each child could then see the colour of all of the hats in front of them, but not their own and none of the ones behind them. They did not know how many hats of each colour there were. Once the puzzle began, they were not allowed to communicate in any way, except to announce what they suspected the colour of their own hat was. Each child who was able to guess the colour of their own hat correctly would get an ice cream. Those who guessed wrong got nothing. After much thought, the children thought of a strategy that would get them more ice cream than simply guessing. What's the best strategy you can come up with?

I will consider this solved once someone comes up with the best possible strategy.

Edited to make it clearer: The children are trying to guess the colour of their own hat.

Edit: Solved by Norroen Dyrd!

Last edited by Moeboid on Tue Jul 23, 2013 11:32 am, edited 2 times in total.

[TopHatKat ●]

I don't think there is a strategy. Why? You never mention what they were trying to solve. Most would assume they are trying to find the number of the colored hats, but it never says so. He just mentions the set up, noone knows their own color, and that they couldn't communicate other than stating what they think their color is. But in the end, the difference between a right guess and a wrong guess is never defined.

I could be wrong on this but I read the paragraph over several times. Never is a goal defined. So how can we think of a strategy?
It's a trick question!

To summarize, we are told that there is a puzzle, but we are not told what it is, so we can't solve it. It's like saying 2_2=? If I don't know what operation to proceed with, how can I solve the problem.

[Moeboid ●]

Edited to make it clearer. Apologies for the confusion. The children are trying to guess the colour of their own hat.

[Musicman247 ●]

My guess:

Spoiler:

They would start at the end, the last child facing all the other children would call out the color hat he could see on the person in front of him. There is a fifty-fifty chance of him being correct about his own hat color and one hundred percent correct about the color of the hat on the child in front of him. The next child would call out the color the child behind him called out, getting ice cream. The next child would begin the process again, calling out the color of the hat on the child in front of him, and so on and so forth to the end. This way they are guaranteed at least half of them will be getting ice cream.

[Moeboid ●]

That's a nice strategy, Musicman. The children could expect well above 50 ice creams using your method, so it's much better than just guessing. You're thinking along the right lines, but the expected number of ice creams can be pushed higher. I'm happy that my question makes sense now haha.

[Musicman247 ●]

Am I correct in assuming

Spoiler:

once a child said one color they would be silenced? In other words the last child couldn't call out all the colors in order, even if pretending to have a hard time making up his mind?

"Black, no, white, no, black, yes, black, wait, white..."

[Moeboid ●]

Yes, you are correct in assuming that haha. I said in the original post that questions shouldn't be misleading. I'm not going to post any questions with trick answers like that. The puzzle is exactly as it seems. Each child says one word, either "black" or "white".

[Musicman247 ●]

Another strategy (if allowed)

Spoiler:

The last child who can see all the hats counts the number of white and black hats and calls out the color of hat that most of the children are wearing. Every child then says the same color. Again they would be guaranteed at least 50 ice creams.

[Lindai ●]

When a child announces a colour, can the rest of the children hear what colour that child chose?

[Moeboid ●]

Musicman, that strategy is allowed, but it's not likely to be as successful as your first one.
And yes, that's correct Lindai. If the children weren't aware of each others' guesses, I think the best they can do is guess.

[TopHatKat ●]

A few of these strats include calling out colors. I thought communications were off limits?

[Musicman247 ●]

You might want to read the puzzle again.

Once the puzzle began, they were not allowed to communicate in any way, except to announce what they suspected the colour of their own hat was.

[Lindai ●]

Spoiler:

The child at the end, who can see everyone's hat, always announces the color that appears most in the line. Let's say it's black. At some point it will change to white. At this point, the children know the ratio of white hats to black hats(50/50). They can then guess every hat correctly after this point by counting how many black hats and how many white hats are in front of them, and by recalling previous announcements.

So every child who guesses up to the transition point has a 50/50 chance of getting it right, and everyone after the transition point has a 100% chance of getting it right. The earlier the transition point, the better. Regardless, if the transition point happens very late, that will mean that every child who has been "guessing" up to then will have a higher chance of being right about their own hat.

Last edited by Lindai on Tue Jul 23, 2013 10:02 am, edited 1 time in total.

[Musicman247 ●]

I'm starting to wonder how old/smart these kids are, because there is no way in heck an average eight year old would figure any of these strategies out.

[Moeboid ●]

Wow, what an interesting solution! Would you be able to edit it and put it in a spoiler? This spoiler contains an analysis of your strategy, Lindai.

Spoiler:

So, if I'm interpreting you correctly, this is what would happen: Let's say child at the back of the line counted more black hats than white hats. They would then announce "Black". Each child in front of them would then do the same thing - count the number of black and white hats - until one of them counted more white hats. This child would then announce "White" (which would always be wrong, I believe). The children would know then know the remaining number of hats of each colour. I agree; they would! If this were to happen early in the line, they would achieve a very high number of ice creams. However, there's a flaw in your logic. You say that that will eventually change to white, but that wouldn't always be the case. For example, if all the black hats were at the front of the line, every single child would see more black hats than white hats, and the accuracy could be very low indeed. Without doing some serious thinking and mathematical calculations, I couldn't even begin to estimate how many ice creams the children could expect to win, but the children could expect about 75% using Musicman's original idea, and I'm inclined to doubt that yours would be higher than that. It doesn't matter much because I can guarantee that the intended solution is better than your strategy. Keep going! You're both thinking along the right lines!

Edit: Yeah, probably not, Musicman. A smart 8 year old might be able to figure out the strategy you suggested (which is probably still in the lead!). The best one? Probably not lol (even if they could, an ice cream isn't worth the amount of thinking involved :p).

[Dark Lord Cam ●]

As they're forming up the line, Child B sneakily trips Child C and makes him smash his head into the wall. While the mom (She didn't notice the trip) is busy tending to his now broken nose, Children A, B, and D peak at their hats. They each call out the correct hat and get icecream. Don't worry about Child C, he stole Child B's teddy bear last night so he had it coming.


Like cutting the Gordian Knot, [&@%!]. /thread

EDIT: I clearly missed that second puzzle. I'll get to it later.

EDIT:

After much thought, the children thought of a strategy that would get them more ice cream than simply guessing.

They charge the icecream truck as one unified unit and swiftly beat up the icecream man taking charge of the steering wheel. They then decide on leaving the old sadistic [&@%!] behind on the road whilst the children make their way to the club house in Timmy's backyard.

The best way to win the game is to not play it at all.

[Blackhawk Vegal ●]

this is my theory

Spoiler:

as the lined up and after getting their hats on, they all march in a straight line pass a mirror or window and called out what color they had on as they passed.

[Dark Lord Cam ●]

Anyways, to answer that second question:

Every child calls out a single color. Assuming the hats are split evenly, they all get 50 icecream to share.

Last edited by Dark Lord Cam on Tue Jul 23, 2013 7:45 am, edited 1 time in total.