DiMono
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You have a hundred bags with a hundred balls each. Every ball in every bag weighs exactly 1 gram, except for one bag where every ball weighs 1.001 grams. You also have a single-balance scale (one platform, and it tells you the weight that's on it) that you may only use once, which measures weights accurately to a thousandth of a gram. How do you figure out which bag holds the heavier balls?

Edit: note, I'm not asking you to set those balls aside, just identify which bag holds them

[Edited by DiMono on 03-26-2004 at 09:05 PM GMT]

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Schik
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Number the bags from 1 to 100. Put 1 ball from bag 1, 2 balls from bag 2, 3 balls from bag 3.... 99 balls from bag 99, and 100 balls from bag 100 onto the scale. Look at the fractional part of the weight (to three significant digits), and that's the bag number that had the heavier balls.


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DiMono
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Wow, 8 whole minutes... at least it was thread reply number 900, that makes it sort of cool... yes?

[Edited by DiMono on 03-26-2004 at 10:46 PM GMT]

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Skylancer64
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zzyzx wrote:
Back in the day, the telegraph was a decent way to send a message, but it was costly. Paid for by the word, one had to be creative to save a buck... Below are three "creative" messages. Can you figure them out?

Have you ever heard of "Ladle Rat Rotten Hut?" See if you can figure it out.

http://tlc.ousd.k12.ca.us/~acody/ladlerat.html

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zzyzx
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Have you ever heard of "Ladle Rat Rotten Hut?" See if you can figure it out.

http://tlc.ousd.k12.ca.us/~acody/ladlerat.html

Priceless. I had never heard of this version of Little Red Riding Hood.
More info here, for those interested:
http://www.crockford.com/wrrrld/anguish.html#Freyer%20Jerker

Schik
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Okay, next puzzle:

Beethro and Bombus are trying their hands at magic. They have a normal deck of 52 playing cards, randomly shuffled. Beethro asks an audience member, Halph, to randomly select 5 cards out of the deck, and hand them to Beethro. The remaining 47 cards are instantly destroyed, never to be seen by anyone. Beethro looks at the 5 cards and gives one of them back to Halph. He orders the remaining 4 cards in some way, and gives them to Bombus. The only information Beethro passes to Bombus is in the ordering of the 4 cards - he doesn't give hand signals, or wink, or use a specific hand, or cough, or anything of that sort.

Bombus looks at the 4 cards and tells Halph the suit and rank of the card that Beethro handed back to Halph.

How do they do this?

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The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

Koro
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Here's an idea:


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Schik
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Dangit, I knew I was going to forget something.

The 4 cards that Beethro hands off to Bombus are all face down. Bombus can of course then turn them over to look at them. The cards are symmetrical, so rotating them won't work either.

Basically, the only information that Bombus can use is the order, values, and suits of the cards.

If you'd prefer, Bombus is in another room, and Beethro tells Halph the order of the four cards, and Halph goes to this other room and tells Bombus the 4 cards, in order.

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The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

noman
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I have a possible solution to this puzzle:



noman

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RoboBob3000
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Schik wrote:

They have a normal deck of 52 playing cards...

...The cards are symmetrical

Actually, in a normal deck of 52 playing cards, there are only 30 of them that are rotationally symmetric.

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masonjason
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404 on your image link, noman.


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Schik
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noman wrote:
Beethro tells Bombus before the game an order of the 4 suits(e.g. Hearts, Clubs, Spades, Diamonds). This order can be used to give every Card in the Deck a rank. Beethro looks at the 5 cards. If 4 of them are in the upper half of the self created ranking, beethro gives the highest card to halph. If there are 4 in the lower half, beethro gives the lowest card to halph. If there are 3 cards in either the higher or in the lower half, beethro gives the highest card to halph. In the worst case, (3 cards in one half) Bombus has to choose from 24(52/2-2) cards. The four cards beehtro hands to Bombus also have a rank. So you can enumerate them (lowest, low, high, highest of them). Beethro can set the order of theese cards. He can arrange theese 4 states in exactly 24 ways(4 for the first card, 3 for the second, 2 for the third, and 1 for the remaining = 4*3*2*1=24). With a little conversation before the game, bombus should be able to choose the right card from the deck.

This doesn't seem to work. Let's enumerate the possibilites for # in each half before and after Beethro gives a cards to Halph:
5 0 -> 4 0
4 1 -> 3 1
3 2 -> 3 1
2 3 -> 2 2
1 4 -> 1 3
0 5 -> 0 4

You have two different configurations going to 3 1, and the card to be guessed is in different halves!



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The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

Koro
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If I secreted this, you would all read it anyway and be irritated for such a lot of reading in an irritating color, so I won't.

Beethro and Bombus select a suit order (Say spades, diamonds, clubs, hearts) so the cards are essentially 1 through 52 (Aces are low) and they are aware that 4 cards have 24 permeutations and know the same logical order for counting them (labelling cards lowest to highest 1234, 1243, 1324, 1342, etc.). All familiar so far, eh? However, when Bombus gets the cards, he notes which card is the highest card (wherever it may be in the order) and uses that as his zero point and counts off the permeutation to the secret card, modularly looping around the deck order if he needs to. Beethro will have chosen the target card and order accordingly. Not all of the cards in a hand of five can be a target, but all will contain at least one. Proof: the five cards will be roughly every 10.4 cards of the deck by probability and therefore a card will easily be in the 24 target range of another card, so bunching distributions must be bad. The worst would be five in a row, but then the highest card is target, and second is zero point, use first pereutation, no problem. If four are together and one is substantially higher it has to be at least 25 cards away to not be hit. If it is it can't be the chosen target and will have to be the zero point if not chosen as target. However, the low cards will be in range because those 4 plus a 25 card distance plus 24 card range is 53 cards. Meaning in worst case scenario, you pick the lowest card as target and are just able to hit it.
Lots of writing, but just a bit more, an example: I have a real deck and am randomly shuffling...
4H, 8S, KD, 6C, 3C
I can pick 4H or 8S as target, nothing else. If I pick 4H, 6C is zero so I encode the number 11 which is 2413 or KD-6C-8S-3C. If 8S, 4H is zero and it is 17 cards (modulo 52) to 8S. This is 3412 or 6C-4H-KD-3C.
Wow. Beethro and Bombus are smart dudes!

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Schik
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I do believe that's a workable solution. Or if it's not, I can't find the flaw in it.

Here's an alternative solution:
There will always be at least two cards of the same suit. Pick any two cards of the same suit, let's call them B and C. Imagine the ranks of cards written in a circle - Ace to King - and look at the two distances around the circle from B to C. One of these distances will always be 6 or less. So take the first card (clockwise) in that shorter distance, and give it to Halph. Put the other card first in the stack to designate which suit Halph's card is. With the remaining three cards, use the 6 different permutations (very similarly to Koro's solution) to tell the distance between the top card and Halph's card.

Regardless, nice solution, Koro! You're up.



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The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

Koro
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Schik, I really liked that last puzzle. The easy solution is really a combo of the two solutions I submitted. So crazy, made me think real hard.
Okay, I ran across this one about 12 years ago in Reader's Digest, and still it has several sites online, so don't look up the answer. Without further ado, Who Owns the Zebra?

There are five houses.
Each house has its own unique color.
All house owners are of different nationalities.
They all have different pets.
They all drink different drinks.
They all smoke different cigarettes.
The English man lives in the red house.
The Swede has a dog.
The Dane drinks tea.
The green house is on the left side of the white house.
They drink coffee in the green house.
The man who smokes Pall Mall has birds.
In the yellow house they smoke Dunhill.
In the middle house they drink milk.
The Norwegian lives in the first house.
The man who smokes Blend lives in the house next to the house with cats.
In the house next to the house where they have a horse, they smoke Dunhill.
The man who smokes Blue Master drinks beer.
The German smokes Prince.
The Norwegian lives next to the blue house.
They drink water in the house next to the house where they smoke Blend.
So, who drinks water, and who owns the Zebra?

I actually need to solve this one myself, too, sometime soon.

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Mattcrampy
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We've had this one.

Matt

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Koro
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No way! I searched for it...
Okay, okay... I'll find something else soon, or somebody else can take it. Seriously, there are thirty-some pages to this topic. Thanks for pointing that out.

We did have a similar one earlier, is that what you're thinking of, because "zebra" search isn't coming up with it.

[Edited by Koro on 03-28-2004 at 04:23 AM GMT]

Okay, I found it. Who Owns the Fish? Not the original title I'm pretty sure. So like I said, new one on the way or somebody else.

[Edited by Koro on 03-28-2004 at 04:35 AM GMT]

Pretty lame one:

What happens every 65 minutes and 27.3 seconds starting at noon every day?

[Edited by Koro on 03-28-2004 at 05:04 AM GMT]

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Drizzo
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------
I don't have a puzzle just yet, and I'm about to go sleepies, if I KNEW my answer was correct I'd find one anyway, but I'm also too tired to do the math, even though I'm pretty sure. Anyway, I'll post a puzzle tomorrow shortly after I get up... but if someone ambitious wants to preempt, well go right ahead... assuming I'm right, that is

[Edited by Drizzo on 03-28-2004 at 07:55 AM GMT]

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Drizzo
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What word would come next in this sequence of words?

STAFF TANUKI ASIAN RABBI THEORISTS


[Edited by Drizzo on 03-28-2004 at 06:51 PM GMT]

It was my 200th post! Yay!


[Edited by Drizzo on 03-29-2004 at 03:40 AM GMT]

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Avon
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or some such.

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"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

Drizzo
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That'll do! I was hoping for Scotch, for the alcohol reference, but if you wanna reference illegal drugs, that's your prerogative, seeing as you solved the puzzle... I look forward to yours, I'm sure it'll be better than mine.


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"Disbelief in magic can force a poor soul into believing in government
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Avon
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Beethro and Bombus are trying a new magic trick. Again they have a normal deck of 52 playing cards, randomly shuffled. This time Beethro asks Halph to randomly select 4 cards out of the deck, and hand them to Beethro. The remaining 48 cards are instantly destroyed, never to be seen by anyone. Beethro looks at the 4 cards and gives one of them back to Halph. He places the remaining 3 cards in a row on a table, each either face up or face down. The only information Beethro passes to Bombus is in the upward-facing sides of the 3 cards - he doesn't give hand signals, or wink, or use a specific hand, or cough, or anything of that sort. The pattern on the back of the cards is preserved under a rotation of 180 degrees and Bombus is unable to see any card's face until Beethro has placed the cards on the table.

Bombus looks at the 3 cards and, without turning any of them over, tells Halph the suit and rank of the card that Beethro handed back to Halph.

How do they do this?

[Edited by Avon on 03-30-2004 at 12:40 AM GMT: add italics]

[Edited by Avon on 03-31-2004 at 06:17 AM GMT: make clearer]

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"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

zzyzx
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STAFF TANUKI ASIAN RABBI THEORISTS
...
STASH

I don't see it. I can see that all the letters in STASH are in the above words, and there might be some pattern to extracting them, or is it something else?

Drizzo
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TripleM
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I saw the start and finish, so knew it had to end in H, but where on earth does the s of starts come from?

Anyway, in the latest card trick, when you say the only information passed is the order and whether each card is up or down or not, if, say, you had all 3 cards down, you wouldn't be able to tell a thing about the order would you? Since he can't turn cards back over?

zzyzx
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Click here to view the secret text

×STAFF TANUKI ASIAN RABBI THEORISTS STASH

(Highlight the secret text above.)

Click here to view the secret text

×STARTS FINISH

(Highlight the secret text above

Okeedoke. The 'S' does seem a bit strange, but the puzzle overall, makes sense.

Drizzo
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Its the only 6 letter word you can make with a START start, perhaps I should have gone for START FINIS, or FIRST and FINAL

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Avon
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TripleM wrote:
if, say, you had all 3 cards down, you wouldn't be able to tell a thing about the order would you? Since he can't turn cards back over?

Yes, that's right. I probably should have written it more clearly. That's what I get for trying to do as little work as possible.

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"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

DiMono
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Alright, here's what I'm thinking:

You will always have at least two cards of one colour, since there are two colours and 4 cards. The first card will go face up, indicating colour, and the second's orientation will detemine whether it's the same suit (up) or the other same-coloured suit (down). Now we have a face-up card and one other left in which to determine the rank.

Now, it's easiest to give rank relative to the first card. There is a 1 in 13 chance of the two cards (first card and chosen card) holding the same rank, in which case the third card will simply go face down. Otherwise, the third card's rank will indicate how many to count up from the first card to arrive at the chosen card (looping around K-A-2 if necessary).

I don't think this is quite right, as there are almost certainly instances where it fails, but am I on the right track?

[Edited by DiMono on 03-31-2004 at 09:01 PM GMT]

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Avon
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DiMono wrote:
I don't think this is quite right, as there are almost certainly instances where it fails, but am I on the right track?

You're on the right track, by which I mean you're trying to find a way for Beethro to tell the suit and rank of a card to Bombus using only the limited means of communication the puzzle allows. But you'll need to make more efficient use of what is available.

____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz