Brain Teasers and Maths Puzzles

[eMTe]

What was the theme of the meeting?

[Zyx]

What was the theme of the meeting?

I wouldn't know. I was doodling and solving a puzzle the whole time.

[eMTe]

Maybe you can give this puzzle to other guys and gals during the next meeting?

Next one.

There's a magical square table on one leg, rotating very quickly. There are four coins lying on the table, one in each corner. Coins are covered with cups. Once in a while the table stops allowing you to make a move. In each move you can pick up TWO cups and either turn to the other side both coins, turn only one coin or leave both coins as they are. After the move you must cover the coins again. If after the move all coins are turned to the same side the table produces jingling sound. If not - table rotates again, stops, you make another move and so on.

What is the lowest possible number of moves you need to make to be ABSOLUTELY sure that you hear the jingle after you cover the coins again?

[Tormuse]

Erm... I'm not sure if I'm understanding the puzzle correctly. If you're asking us to predict what side the coins will land on when we toss them each time, then I don't think there's an answer, because it's impossible to predict that many coin flips ahead of time. Or, if you're asking us to assume that, by luck, we get the correct coins turned up and they land the way we want them to, then the answer is 2 moves; one for each pair of cups to make all four of them.

I suspect that neither of those is correct and there's just something I'm misunderstanding here.

[eMTe]

I suspect I am to blame, because I probably used the word "toss" in a wrong way - I thought it can be used also as "turn to the other side". Sorry!

Puzzle edited.

[Tormuse]

Okay, that's a lot clearer. Thanks!

And yes, "toss" means to throw. Also, in English, the phrase, "flip a coin" is often used to describe throwing a coin in the air so that you don't know what side it will land on. I'm glad you reworded it to say turn to the other side.

I'll give it some thought and post again later... (unless someone else beats me to it)

[Tormuse]

Oh, crap! I forgot about this! Okay, hmm... My first thought was that if it's really random which side comes up, then we might never win because the correct coins might not come up, but I'm not giving up that easily, so I'll work backwards and see what I can come up with...

Each time you do a move, you can either pick up two cups on the same side, or two diagonally across from each other. Picking up the ones on one side means you have four possibilities of cups to pick up, (for each side of the square) but picking up the ones on the diagonal gives you two possibilities, so, the way I see it, I have to somehow arrange the coins so that there are two heads diagonally across from each other and two tails on the other diagonal. That way, for my last move, I can pick two on the diagonal, turn them both over, and know that I will get the jingling sound.

So, with that goal in mind, here we go... (This all assumes that the starting arrangement of coins is not already all heads or all tails)

First move: Pick two on the diagonal. They can either both be heads, both be tails, or one head and one tail.

Branch 1: Both heads. (note: for this branch, you can switch all instances of "heads" with "tails" and vice versa for the same result)

If you turn both coins to tails, there are two possibilities: Either both unknown coins are tails and you'll get the jingling sound, or the two unknown coins have one head and one tail. If we don't get the jingling sound here, that means that you now know for sure that the table has three tails and one head.

Second move: Pick two on the diagonal again. If it's one head and one tail, then you turn the head over and you know you've won. Otherwise, you turn over one of the tails to head and you now know that two heads are on one side of the table and two tails are on the other.

Third move: Pick two on the side. If they're both the same, turn them over and you've won. Otherwise, turn them both over anyway and you're guaranteed to have two heads on the diagonal and two tails on the other diagonal.

Fourth move: Pick two on the diagonal. Turn them both over. Win!

Branch 2: One head and one tail.

Turn them both to tails. If you get the jingling sound here, that means the two unknown coins were both tails and you've won. Otherwise, you know that the table has two tails on one diagonal, and the other diagonal is either two heads or one head and one tail.

Second move: Pick two on the side. One will be tail and the other will either be head or tail.

Branch 2.1: Both tails.

That means that the other two are a head and a tail. Turn them both over to heads and you'll be guaranteed to have three heads and one tail on the table. From this point, you use the same formula for Branch 1, move 1, and you'll be sure to win by the fifth move.

Branch 2.2: One head and one tail.

Turn the head to tail. If you get the jingle here, you've won. Otherwise, you know for sure that the table has three tails and one head and you can use the formula from Branch 1, move 1 to win by the fifth move.



So, I guess that's my answer: Five moves! But it could be four moves if you're lucky and get two of the same on the first move. (It's possible that there's a more efficient answer; I'll give it some more thought and maybe I'll edit this later)

EDIT: The more I think about it, the more I realize that there are multiple possible ways of solving it, but I can't seem to come up with anything more efficient than five moves, so I'm sticking with that answer.

[eMTe]

Ill read your answer when I come back from work, I hate reading lengthy posts at this time of the day.

But it looks like you studied this puzzle carefully, so your answer is probably right. I will check the forum where I found it though. Gotta admit I didnt solve it myself - I simply found it together with solution and thought it is worth posting in this topic.

[eMTe]

The guy in other forum also beat it in five moves, so I guess this is the solution.

[Tormuse]

Nice puzzle, eMTe! It was fun to figure out.

Here's another one, of the lateral thinking variety:

Two coal miners finish a hard day at work. One of them comes out of the mines absolutely filthy from head to toe, while the other one is completely clean after coming out of the mines. The clean one showers and changes his clothes before heading home, while the filthy one just heads straight home and goes to bed without cleaning himself.

Why?

[eMTe]

I think I read this puzzle years ago, but I dont remember the solution, so Ill be wildguessing. I dont know, one of them is manager? It's some special kind of mine?

[Tormuse]

...one of them is manager?

No, they're both the same type of worker.

It's some special kind of mine?

No, there's nothing special about the mine. One of them just happened to be cleaner than the other after work.

[eMTe]

I'm thinking...and probably this is the problem.

[Tormuse]

Probably.

Okay, a hint... (It's hard to think of a hint that doesn't give it away!) They both value cleanliness, but there's a logical reason they behaved this way.

[eMTe]

Ah, so there's some logic behind this laterality after all.

[Tormuse]

Well... I guess I use the word "logical" loosely here. I mean... I still think that blue eyes puzzle has questionable logic to it, but if the answer to it is considered logical, then this puzzle's answer can definitely be considered logical too!

Seriously, though, think about it... If they both value cleanliness, why would the one who is already clean wash himself, but not the one who is dirty?

[eMTe]

Maybe words "clean", "filthy" and "mine" in this puzzle depict not physical states and object, but mean something *cough* different? Im thinking too lateral here I suppose.

[Chroelle]

The filthy one lives in the mines? Then there would be no reason to shower before heading back in...

[eMTe]

Yeah, but it doesnt explain why the other one is clean if he does exactly the same job and in the same mine.

[Tormuse]

Maybe words "clean", "filthy" and "mine" in this puzzle depict not physical states and object, but mean something *cough* different? Im thinking too lateral here I suppose.

Nothing like that. There aren't any unusual meanings for the words. By "clean," I just mean that he's as clean as any regular person out on the street. By "filthy," I just mean that he's visibly very dirty from coal dust. By "mine," I mean a big hole in the ground where miners go to work to mine for stuff.

The filthy one lives in the mines? Then there would be no reason to shower before heading back in...

No.

Yeah, but it doesnt explain why the other one is clean if he does exactly the same job and in the same mine.

I'm going to highlight this comment for no particular reason.



I'm surprised that Zyx hasn't weighed in on this puzzle yet; I'm sure he could come up with some good guesses.