DiMono
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Wow, 18 minutes. You're up.

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bibelot
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Here's a semi-classic:

In a tall tower there are a hundred wires installed from its top to its bottom. You've been hired as electrician to label their ends so that they can be used later. Of course, all the wires are the same color and they are embedded in the wall so you can't just follow each wire up to the top of the tower. All that you have besides a set of labels is a (small) device that can tell you if the ends of two wires are joined by a circuit. You can also join and unjoin the ends of any two wires at the same end of the tower. What's the fewest number of trips up and down the tower that you can take to label all the wires correctly?

DiMono
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Are we allowed to tie more than two wires to each other? i.e. can we tie three together?

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bibelot
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DiMono wrote:
Are we allowed to tie more than two wires to each other? i.e. can we tie three together?

Sure.

DiMono
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Alright, I'll say 50 trips both ways. Tie all but one together at the bottom, go up, and test until you find a broken circuit. That's 1 identified. Rinse and repeat.

Probably not the optimal solution, but I may as well put it out there.

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Koro
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I believe I have a one round trip solution:
On the ground floor, (presumably where you enter the problem from) connect wires to make 48 pairs, a group of three, and a lone wire. Label the lone wire with a little drawing of Beethro.
Head up to the top.
Test wires like crazy, and group wires together that tested positive for the circuit. You should end up with 48 pairs, a group of three, and a lone wire. Start by labelling the group of three with 1-A, 1-B, 1-C, and then the pairs 2-A, 2-B, 3-A, 3-B... 48-A, 48-B, 49-A, 49-B. Whew. Now draw Beethro on the stray wire. Connect him to 1-A, connect 1-B to 2-A, connect 2-B to 3-A... connect 48-B to 49-A. Now you have 49 new pairs and two stray wires: 1-C and 49-B.
Go back down.
Label stuff as you learn it. Beethro will test positive with a wire in the group of three, which you can now label 1-A. 1-C is another wire in the group of three that does not work with any other wire in the room. The third wire, 1-B of course will only find one mate, 2-A. The wire 2-A was previously combined with can be labelled 2-B. Find its match and call it 3-A, its previous partner is 3-B, which will test positive with 4-A in the room.... you get the idea.
Man this took me a while. Let me know if I'm right.
Koro

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bibelot
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Looks good.

sims5000
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your go Koro

Koro
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What do monsters do in their free time? That is, when they're not trying to eat Beethro?
Two brains are in a large room with three roaches. One brain challenges the other to guide the roaches from their starting cartesian coordinates of (0,0), (0,3), and (3,0) to the coordinates (-1,1), (2,5), (-1,3) under the following stipulations:

Only one roach may move at a time.
The moving roach must travel along a line parallel to the line defined by the positions of the other two roaches.
Roaches may move any distance in either of the two directions available to them for their move.
Roaches may be moved in any order. (1,2,3,2,3,1,3,1,2, etc. doesn't matter)
This problem doesn't follow the limitations of a DROD tile floor in that the roaches may be at any position, even those with fractional coordinates.

Is this possible? If so, how? If not, why not? This is not as mathematically complex as it seems. The answer will be short.

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TripleM
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Koro
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You got it buddy!
Let's see your puzzle!

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TripleM
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Hmm, its getting harder and harder to check puzzles haven't been posted before..

The game "double chess" is like normal chess, except each player makes two moves for their turn. (However, if your first move is to check the other player, thats the end of your turn). Can black (the second player) force a win?

DiMono
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I'm going to say the game always ends in a draw. The only way to checkmate the opponent is to control 25 of the 64 squares, or 15 if the king's against the wall. However, since there are always two moves after each check, an intelligent player will always be able to negotiate away from the edge of the board.

Now, the only way to negotiate a checkmate would be to line up your two rooks and queen so they each occupy consecutive rows, which will then force the king toward the side of the board, but it's a simple matter to take out one of the two rooks during the game, so you can always force a draw.

Of course, this assumes that if you're in check then you're not considered to have moved in to check until after your second turn (in check, first move still in check, second move not in check end turn). If that assumption is invalid, then so is the logic of this post

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TripleM
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Yeah, the king can't be in check at all after either move, similarly to the way your move will end if you check someone, so you are going to have to try something else..

In fact the original problem doesn't say anything about kings being in check, but people always try to find problems with the game actually working, so I've added that in.

The_Red_Hawk
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DiMono, there are many more ways to checkmate than the one you mentioned above.

I'm pretty sure there are a lot of ways for either player to force a win. Unless you mean that every single moveis forced?

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TripleM
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If you want to know the actual answer,


Now prove it

Oneiromancer
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It's been a couple days now, so if there's anyone out there that knows the actual answer already, and wants to post and put their own puzzle up, now's the time. If not, I've never thought about what kind of time frame is allowed to declare a puzzle unsolved...probably about a week, I'd say, so no worries yet.

Game on,

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DiMono
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I'm going to say that nobody can "force" a win. When one player puts the other in check, the other player has a move in which to get out of check, and then another move to do with as they please. The basis of "forcing" is that once the opponent relieves the check, you put them in check again. Since the opponent, in this case, gets to move before you, you cannot establish a force in this way, so nobody can force a win.

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eytanz
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That doesn't preclude a possibility where you can force a win by putting someone in a check he can't get out of (because every move he makes would leave him in check).

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bibelot
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There's a classic argument one can use here; the answer doesn't depend that much on the specifics of the game of chess.

eytanz
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If I'm right, it depends on at least one specific.

Black cannot force a win.

For black to be able to force a win, she must be able to defeat white not matter what he does in the first turn.

However, white can move a knight back and forth in his first turn, resulting in a move that did nothing. Black is then in the same position white was before he moved. If there's anything that black could do at this point to force a win, white could have done it first.

Ergo, black cannot force a win. QED.

(The reason it depends on the nature of the game is because if there was no zero-sum move that white could make in his first turn, the logic would fall apart).


[Edited by eytanz on 02-28-2004 at 02:47 AM GMT]

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TripleM
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Thats correct.

eytanz
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Well, Bibelot can have it if he wants it, since he obviously knew the answer.

Otherwise, I'll post a new puzzle after the weekend - I have a major paper deadline on Monday and I can't spend the time looking for a new puzzle, nor does any come to mind at the moment.

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eytanz
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Oops - forgot that it was my turn. Anyway, here's a small and silly puzzle originally posted by Andrew Jenner on rec.puzzles:

My pet monster gets very hungry but is a bit dim and can only communicate with numbers. If he wants a bird to eat he grunts "10", if he fancies vegetables it's "16", for an insect he mumbles "2" and if he's thirsty and wants hot drink he grunts "20". What should I do if he wants a "21"?


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DiMono
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21 is 12 backwards. I'd give him an insect, then a bird.

Alternatively, I'd just go buy a new monster.

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eytanz
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That's not it (at least I don't think so). I think I'll require an explanation of why you choose to respond in the way you do.

Hint: the numbers aren't random.

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agaricus5
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Are the numbers in base 7?

If they are, then give him a vegetable, and then an insect.

Oops - Forgot that I'm not allowed to post solutions if I haven't got a puzzle.

Sorry. Ignore me.

[Edited by agaricus5 on 03-04-2004 at 11:41 PM GMT]

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Koro
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I'm just gonna do a little thinking out loud, maybe it will give someone the pieces they need to solve this thing. I for one, am stumped. To review:
10 - bird
16 - vegetables
2 - insect
20 - hot drink
21 - ?

I at first was looking for various manipulations in different bases, but one would think there would be something in the problem to imply that. Base 7 seems just a little too random. I messed with base 2 since the word "bit" was in the puzzle. Also found no correlation there. As far as adding up stuff goes, like half a bird and vegies, or half an insect and hot drink, the puzzle shows no use of this in previously defined objects, so I think the 21st object will be something completely new, so long as it fits rules followed by the other objects. I've played around with the numbers representing letters or word size, no luck, so the best I can tell is that the numbers might be some sort of relative size or weight. Thus, the insect has the tiniest number, we suppose a vegetable is a bit larger than a bird (this could vary by specifics). So the twenty-first object is a bit larger than that mug of hot drink. So my guess is a sandwich.
Koro

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eytanz
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Ok, since everyone is a bit off-base (no pun intended), I'll give a hint:

This puzzle doesn't involve any math tricks. Try to figure out why these particular numbers - the choice between each number and what you give the monster isn't arbitrary. And as I mentioned in the first post, this puzzle is rather silly; every response so far is thinking on too complex a level - if you can't figure it out, try applying more basic skills, rather than more advanced ones.

[Edited by eytanz on 03-06-2004 at 04:19 AM GMT]

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DiMono
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Hahaha, I got it. You should give him a hug (or else feed yourself to him).

insect is 2: B
bird is 10: J
veggie is 16: P
drink is 20: T
21: U: You!

I'll come up with a puzzle shortly

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