zzyzx
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Could positioning help? For instance, if two cards were less than a card's width from one another, or further away, or if they touched in any way... Or would this fall under the no winking/coughing clause?

Avon
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zzyzx wrote:
Could positioning help? For instance, if two cards were less than a card's width from one another, or further away, or if they touched in any way... Or would this fall under the no winking/coughing clause?

This falls under the no winking/coughing clause.

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Drizzo
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I haven't really put much thought into the puzzle yet, and probably wont before someone else answers, but I assume that these cards are not square and a rotation of 90 degrees would be legal within these rules, since you pointed out that they were rotationally preserved at 180 degrees... that certainly would increase the amount of communication available rapidly... for example, DiMono's first suggestion as to the color of the card, you wouldn't need the second card to be used, just rotate the 1st card 90 degrees if it were the same color but different suit... Hmm... yep... still too lazy to finish the puzzle, mainly because I can't come up with another one as good right now, but it wouldn't be too difficult at all w/90 degree rotations allowed... and if you could space the cards differently too then it would be far too easy... heh, if you placed them on a square table, and used which corners they were placed in as communication you could probably do it with 3 cards...
---------
Edit:actually give me the ability to position it on a table and one card with one side red and the other side black, nothing on it, and I'll communicate any card that a spectator tells me to, with only which side is facing up, the orientation of the card, and whether its in the corners, on the sides, or in the center.
3 orientations * 9 positions * 2 sides = 54


[Edited by Drizzo on 04-01-2004 at 01:20 AM GMT]

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Avon
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Drizzo wrote:
I assume that these cards are not square and a rotation of 90 degrees would be legal within these rules, since you pointed out that they were rotationally preserved at 180 degrees

I wrote:
The only information Beethro passes to Bombus is in the upward-facing sides of the 3 cards.

I meant this sentence to prevent any information being passed by rotating cards, and put in the 180 degree comment to explicitly prevent the most obvious rotation. If you like we can have the cards being circular with completely black backs.

Schik didn't write:
If you'd prefer, Bombus is in another room, and Halph goes to this other room and tells Bombus what was on the upper side of each of the 3 cards, in order.
but if this was his puzzle, he very well might have.

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Koro
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I take it there is a solution to this? I have devised a solution that works with 97.7% of all possible deals. I don't consider that a valid solution. You aren't relying on probability here are you? I gotta be close here.

[Edited by Koro on 04-05-2004 at 01:57 AM GMT: My percentage was wrong]

[Edited by Koro on 04-05-2004 at 03:02 AM GMT]

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RoboBob3000
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Yeah, I think this has sat long enough to be considered as "given up". Unless Koro is possibly on the right track, I'd like at the very least some sort of hint.

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Drizzo
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I don't know about that, Crampy's puzzle sat longer than this before he even gave out hints. Of course this is a logic problem, which normally I would expect solved by this group in 10 minutes, as opposed to a more obscure word problem.

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Avon
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Koro wrote:
I take it there is a solution to this? I have devised a solution that works with 97.7% of all possible deals. I don't consider that a valid solution. You aren't relying on probability here are you? I gotta be close here.

I've been meaning to make a post on this thread. There's definitely a solution. You could post your almost solution for discussion, unless you're afraid of someone modifying it and solving the puzzle. However such a person would probably let you go next. If you don't want to post it I could try and think of a general hint, but that might not be very much use.

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Koro
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Okay, I got it! I tweaked my old system so now it works 100%!

So here goes:
You are Beethro. If there are two or more cards of the same rank in your hand, pick one of those for your target card and give it to Halph. Leave that card face up and turn the other two down. Now the cards can be represented in three ways, with the face up card in any of three positions. This represents which of the three remaining cards is target (since obviously the face up card disqualifies that suit). This has been discussed with Bombus before hand and a suit order is established. So this is the preferred method, but it can only be used if there are two or more of the same rank.
A more diverse hand is much more complicated. Three cards face down reveals nothing, except perhaps a single card, maybe the Joker? Two cards down is a system already taken and used as efficiently as possible I believe, So the only advantage of card flipping will be with one or zero down. This results in three locations for a flipped down card or all face up. So it seems a good idea to use this to reveal suit (i.e. Spades=Down, Up, Up, Diamonds=UDU, Clubs=UUD, Hearts=UUU). But really you do need a proxy card for flipping down so you only have two to really work with to show the rank of your target card and the third card will be disregarded if the suit is hearts. So I was hoping that there would be some cool property such that 13 Choose 4 contained cards that two of them could add up or subtract down or multiply to one of the other cards. Well it isn't nearly that simple. Some of the simpler rules get you to say 691 of the 715 rank combinations which is where I got my 97% earlier. But anyway, the rule is that out of your four cards (if there are no repeats, but that is already taken care of) you will always be able to find three cards A, B, and C such that (6A+8B)mod13=C. Finding that is another thing. So Bombus notes if a card is faced down, where it is, and then adds the first face up card times 6 to the second times 8, divides by 13, and takes the remainder for rank.
I am pretty sure this will work, but I will still wait for confirmation before I post a puzzle (which will pail miserably in the light of this beauty).

[Edited by Koro on 04-05-2004 at 07:36 AM GMT]

This just in: besides 6 and 8, 3 and 11 work too, as well as an infinite amount of other numbers mod this or that, but these are the lowest and they both add to 14. Hmmm...

[Edited by Koro on 04-05-2004 at 07:41 AM GMT]

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Avon
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Koro wrote:
Okay, I got it! I tweaked my old system so now it works 100%!

That's amazing! Your way works and is almost completely unlike my intended solution which was:

Divide the cards into 3 "suits" of 17 cards with one odd card over, say
"Suit" 1: A-K of H, A-4 of S
"Suit" 2: A-K of D, 5-8 of S
"Suit" 3: A-K of C, 9-Q of S
Odd Card: K of S

If the odd card is among the 4 cards, give it to Halph and put the other 3 cards face down. Bombus looks really amazing, guessing Halph's card with no information.

Otherwise there must be at least 2 cards of the same suit. Also since the suits have 17 cards, one card from this suit can be reached from another by counting forward (returning to the start if you count past the end) at most 8 cards. Give this one to Halph. The leftmost face-up card will be the starting point for the counting. We encode how far forward to count as follows: DDU = 1, DUD = 2, DUU = 3, UDD = 4, UDU = 5, UUD = 6, UUU = 7 if the second card precedes the third in some agreed upon linear ordering and UUU = 8 otherwise. So Bombus looks at the leftmost face-up card, works out the number and counts forward to the card Beethro gave Halph.

But anyway, you solved it so you're up.

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DiMono
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Wow, Koro's solution blows my mind. Parts of my brain matter are sitting on my screen right now, sliding down it at a semi-constant rate. Bravo!

(wow, I'm saying things like bravo a lot on these forums lately. I must be jonesing for pasta)

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Koro
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Beethro is walking along a raised catwalk over a bottomless pit. each board that makes up this walkway is 1 foot by 9 feet by a couple inches, arranged so that the walkway is 9 feet wide and Beethro encounters one board at a time. There are sturdy boards on the walkway that have poor foundations and any weight put on them will cause them to immediately plummet, unlike DROD trapdoors where Beethro can step on them first and they fall after he leaves. Beethro can stretch his step to 4 feet across, but a sprained ankle he acquired in a recent magic show with Bombus (too much math can do that ya know) keeps him from jumping or stepping further.
The walkway's boards are as follows with Good and Bad foundations.

G G G B G G B B B G G B B B B B B B B B B G G B G G G

How does Beethro get across?

Extra puzzle info: No rope, no sword, very good board strength, very good friction, Beethro is pretty tall and strong, common sense dictates what else can be used... etc.

[Edited by Koro on 04-05-2004 at 11:25 PM GMT: Added an extra B to the largest gap]

[Edited by Koro on 04-06-2004 at 12:13 AM GMT]

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zzyzx
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If any weight causes the board to fall, could he do the following?

I am assuming he doesn't know which boards are loose, so he tests along the way. He gently presses with one foot on each of the boards until he reaches board number 4. That board starts to fall, but Beethro grabs onto it and pulls it back up. From that point on, he uses the board to test the sturdiness of each future board. So he steps over the hole created by board number 4 (being able to step 4 feet), and tests #5. It's good, then 6, and it's fine as well. He moves forward and tests #7. It falls, but that's ok. He presses 8 and 9 and they both fall. Testing 10 proves sturdy, so he steps over the 3 foot gap. He follows the same method till he gets to #15. At that point, the gap is to big to step over, but he's got the 9 foot board with him. He uses it to test each successive board until he hits 21. He should have no problem testing 21, with a 9 foot board + arm reach. It is sturdy. So he uses the 9 foot board (plus inches, per the description) to bridge the 9 foot gap. He walks across, picks up the board and using the same method from before, gets across.

This solution looks too easy, am I not understanding the puzzle?

[Edited by zzyzx on 04-05-2004 at 10:39 PM GMT]

Koro
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You understand the puzzle very well. However, a 9 foot board will not bridge a 9 foot gap; it will fall through. I said 1 foot by 9 foot by a couple inches, not and a couple inches to give the boards an unimportant thickness. You will have to do something trickier to cross the big gap.

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Scott
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Turn the board a bit because the diagonal is more than 9 feet.

Koro
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The board's diagonal is the square root of 82 feet which is 9.05 feett or 9 feet and two-thirds of an inch which leaves a third of an inch on each side of the gap. "Very good friction" probably still isn't good enough for this to work. But to catch this and further trivial answers, I have added an extra foot of bad board for good measure.

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agaricus5
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It's a silly suggestion, but anyway...

If the boards are very heavy, about 2 1/3 times Beethro's weight (You did say Infinite Strength which I guess refers to Beethro, not the boards), Beethro would carefully test each board until he reaches the twelfth like before, grabbing each bad board before it fell. Beethro would continue testing the next ten boards in reach (With a board and his arms)and find them all bad. He then places one plank balancing out into the gap, with 8 feet of it over the gap and one foot over the eleventh plank, and then puts the other three on top of the part over the eleventh plank, so it will balance him (The pivot is at the edge of the eleventh plank). Beethro carefully walks out to the end of the plank and tests the next plank by reaching out with his foot, and finds it solid. He then continues on, testing the next planks and avoiding the bad one, finally ending up on the other side.

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Koro
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It's a silly suggestion, but anyway...

Those three boards together would have to equal a little over 7 times Beethro's weight based on where the fulcrom is. Oh, rereading your post I see that you knew that. Yeah, I think that falls under the common sense clause. I will elaborate on that clause in that I have actually done this on a ropes course (granted I was three feet above some dirt and not over a bottomless pit), but it is a bit difficult to bring a physical puzzle down to text. But there is a nice, clean answer out there.

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DiMono
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The boards are very strong, and Beethro is not naked. How about he tests the boards as he did before, collecting two of them, and when he reaches the long sequence of bad supports he takes off his pants and shirt and wraps them around the two boards he's collected, making them a combined ten feet long, then crosses on them, collects them and his clothes, and continues on his merry way?

[Edited by DiMono on 04-06-2004 at 12:03 AM GMT]

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Koro
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Alone in my apartment, I laughed my head off out loud. Oh man...<wipes away a tear>...
Well, that is a very good and funny answer. We could say that this violates the no rope clause, his clothes are too flimsy, or that Beethro has some propriety not to do this. Or we could say it all works just fine and you post the next puzzle. I leave it up to you all. (And there is another answer in which Beethro stays fully clothed.)

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DiMono
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I'd like to see the real answer, and then if whoever gets it wants to defer the next puzzle to me then I'll post a fun one.

Edit: How about he uses one of the boards in a pole vaultish way? Or, since he's very strong and there's lots of friction, as stilts?

[Edited by DiMono on 04-06-2004 at 12:18 AM GMT]

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Koro
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No and no. Sprained ankle eh? Or something. but such acrobatics are not required.

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zzyzx
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What about a cantilever?

      A     B C D
G G G B G G B B B G G B B B B B B B B B B G G B G G G

If you drop/catch boards A,B,C,D it leaves two holes in the bridge. Using one of these boards, you pass through hole A, down and under the bridge, and pull (hard) up through the second hole at BCD. If you continue to pull the board through, you get two feet of board past hole BCD, with one foot of board behind hole A. You can then use one or more (for strength) boards placed under the lip of the bent board as it projects out from hole BCD. The diagram below shows the boards, with '*' being the bent board and '#' being the stack of boards for rigidity.

                    *
    *             *##################
G G G * G G * * * G G B B B B B B B B B B G G B G G G
        * *  

If Beethro was light enough, and did not jump up and down, he could, theoretically, just possibly, walk the plank, and step over the gap of the two last bad boards. He could also, step earlier if his plank starts to bend, which it most definitely will.

Schik
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Building off of zzyzx's solution:

                          # #
                        * *   # # #
                  * * *             # # # #
G G G . G G * * * G G B B B B B B B B B B G G B G G G
          * 

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Koro
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File: bridge.bmp (127.9 KB)
Downloaded 112 times.
License: Other
From: Unspecified

Again, for zzyzx's solution to work the force on the short end of the board behind the fulcrom has to be about 7 times Beethro's weight. Schik's solution works, and is similar to my intended solution, so he is up. The way I did it is in the enclosed bitmap. It isn't to scale, but Beethro can reach out and place the red board, then slide the blue and green boards in with his other hand so they all rest on each other and walk across the bridge. Good job Schik, you're up.

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zzyzx
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Yeah, but mine was fancier...

Schik
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Next puzzle:

Neil wrote a letter to an overseas friend. He addressed it in the following cryptic fashion.

Wood, S
May
England

What is Neil's friend's name and address?

Note: This is (probably) not a real address. Using mapquest or something won't help. At least I don't think it will.

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The_Red_Hawk
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S. Wood, in the town of May, England?

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Schik
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The_Red_Hawk wrote:
S. Wood, in the town of May, England?

No. There will be a first and last name, street address, city, and country.

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krammer
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Are the town/city and country real places, or just made-up real sounding places? I think I've got the name, but if the town is real it would narrow things down a lot...

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