UESP Forums

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

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

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

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.

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?

You certainly may

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

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!

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.

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

My guess:

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.

Am I correct in assuming

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".

Another strategy (if allowed)

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

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.

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

You might want to read the puzzle again.

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.

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.


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).

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:

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.

this is my theory

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.