Math Puzzles (Read the Rules!)

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Math Puzzles (Read the Rules!)

Postby Timko » Thu Apr 15, 2010 8:47 am

Since Chuck missed out of the last math "puzzle," I figured I'd start a thread of them.

Here are the rules.

1. The person who answered the last puzzle HAS to ask the next one. If you don't want to play, then don't reply.
2. Show your work.
3. Please try to keep math out of high level topics (this is mainly directed toward me). Comp Sci and Math problems are both acceptable.
4. The current question must be answered and validated before moving o to the next one.

- - -

Someone showed me this problem on Tuesday. Aside from an answer, I'd be interested in how you figure out the problem.

This was from my 'revolt of the lab rats' series and it was sent in interestingly enough by a fellow named Andrew Magliozzi, who happens to be my son! I thought the name looked familiar. (Web lackey note: Andrew insisted that we shamelessly promote his commercial enterprise, Veritas Tutors, in exchange for this mediocre brain teaser. Though it sounds sleazy to us, he is the boss' son, so we do what we're told.)

Imagine this: It's the eve of the annual Car Talk 'We Haven't Been Canceled Yet' Banquet. John 'Bugsy' Lawlor has procured the food and the wine for the following evening's gala, and he's extremely pleased with himself because he knows a guy, who knows a guy, who knows a guy, and he's obtained for $50, thirteen one-half gallon jugs of the finest red wine. He's very excited about the following evening's festivities until Doug 'Punkin Lips' Berman informs him that he received a note suggesting that one of those 13 bottles of wine contains a deadly poison. In fact, it's one that kills within 24 hours. 'Is someone out to get us? Who could be out to get us? Why? Why not? But why the whole staff?'

Anyway, because they're hopeless cheapskates and unwilling to discard 12 bottles of perfectly good cheap wine, they head off to MIT to consult with a scientist friend of theirs. 'So let's see,' he says, 'you have these thirteen bottles of wine and one of them contains a poison that will prove fatal within 24 hours after it's been consumed. And the Car Talk Extravaganza is when?'

'Tomorrow night.'

The scientist goes on to suggest that from his knowledge of poisons, even the smallest sample is usually enough to cause certain death, even if mixed and diluted with the wine from the untainted bottles. 'Hmm,' he says, 'I'll be right back.'

In a flash, he returns with four small cages, each one containing your standard lab rat. What a moral dilemma, they think, we have to sacrifice lab rats to save Car Talk? 'But wait, wait,' they say. 'We have 13 bottles of wine. How are we supposed to save the entire Car Talk staff and empire, with just 4 rats?'

'You can do it,' he says and then disappears into the inky shadows.

So, you have 4 rats in little cages, 13 bottles of wine and one of them has got poison in it. Now you can obviously take samples from any of the bottles and you can give as much or as little as you want to any of the rats. And don't forget, you're not going to know if the poison is fatal until the night of the banquet because it takes 24 hours to kill human or rat. So, how do you do it?
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Re: Math Puzzles (just for Chuck)

Postby dgdave » Thu Apr 15, 2010 8:50 am

Can I answer?
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Re: Math Puzzles (just for Chuck)

Postby Monocacy » Thu Apr 15, 2010 9:18 am

dgdave wrote:Can I answer?

Can I?
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Re: Math Puzzles (just for Chuck)

Postby Timko » Thu Apr 15, 2010 9:34 am

Of course. Just remember, SHOW YOUR WORK! Math is a process, not an answer.
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Re: Math Puzzles (just for Chuck)

Postby dgdave » Thu Apr 15, 2010 9:48 am

Keep eliminating 1/2 the bottles.

Take mouse1 and sample 6 bottles. If he lives, m1 samples the other six. If m1 dies, have m2 sample 3 ofthose bottles. He lives, move to other 3, he dies m3 samples 2 of them and so on.
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Re: Math Puzzles (just for Chuck)

Postby NoLifeLeft » Thu Apr 15, 2010 9:49 am

Label your rats A-D. Label your wine 1-13.

Chart 13 combos of rat death.
1-All
2-A
3-B
4-C
5-D
6-A&B
7-A&C
8-A&D
9-B&C
10-B&D
11-C&D
12-None
13-A,B&C

Using the chart give each rat wine as follows:
A-1,2,6,7,8,13
B-1,3,6,9,10,13
C-1,4,7,9,11,13
D-1,5,8,10,11

Wait for death and compare results.

Enjoy the other 12 bottles of wine.
Last edited by NoLifeLeft on Thu Apr 15, 2010 3:41 pm, edited 3 times in total.
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Re: Math Puzzles (just for Chuck)

Postby garublador » Thu Apr 15, 2010 9:52 am

Timko wrote:Since Chuck missed out of the last math "puzzle," I figured I'd start a thread of them.

- - -

Someone showed me this problem on Tuesday. Aside from an answer, I'd be interested in how you figure out the problem.

At a party, there are 12 bottles of wine. However, 1 of these bottles is poisoned. Luckily, you have 4 rats to help you determine which bottle of wine was poisoned. How would you determine the poisoned bottle?
I'm totally missing the point of this one. Can you only feed each rat wine one time? Why not just test the bottles until one of them kills one rat? What are the other three rats for?
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Re: Math Puzzles (just for Chuck)

Postby Timko » Thu Apr 15, 2010 10:12 am

Updated the description. Sorry; I only saw this one in passing when talking with a teammate.
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Re: Math Puzzles (just for Chuck)

Postby NoLifeLeft » Thu Apr 15, 2010 10:21 am

Timko wrote:Updated the description. Sorry; I only saw this one in passing when talking with a teammate.

Fixed prior post for new description.
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Re: Math Puzzles (just for Chuck)

Postby Timko » Thu Apr 15, 2010 10:23 am

NoLifeLeft wrote:Label your rats A-D. Label your wine 1-12.

Chart 13 combos of rat death.
1-All
2-A
3-B
4-C
5-D
6-A&B
7-A&C
8-A&D
9-B&C
10-B&D
11-C&D
12-None
13-A,B&C

Using the chart give each rat wine as follows:
A-1,2,6,7,8,13
B-1,3,6,9,10,13
C-1,4,7,9,11,13
D-1,5,8,10,11

Wait for death and compare results.

Enjoy the other 12 bottles of wine.


On point. Here's my solution.

Wine numbers in binary
1 - 0001
2 - 0010
3 - 0011
4 - 0100
5 - 0101
6 - 0110
7 - 0111
8 - 1000
9 - 1001
10 - 1010
11 - 1011
12 - 1100
13 - 1011

Since 13 can be represented in 4 bits (the same number of rats you have), you can use those bits to determine which rat gets what wine.
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Re: Math Puzzles (Read the Rules!)

Postby Timko » Thu Apr 15, 2010 10:26 am

NoLifeLeft, the ball is in your court.
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Re: Math Puzzles (Read the Rules!)

Postby chiggins » Thu Apr 15, 2010 10:31 am

Workin' off No Life Left's truth table:

4 rats die: can test 1 bottle on 4/4 rats (abcd)
3 rats die: can test 3 bottles on 3/4 rats (abc/abd/bcd)
2 rats die: can test 6 bottles on 2/4 rats (ab/ac/ad/bc/bd/cd)
1 rat dies: can test 4 bottles on 1/4 rats (a/b/c/d)

1 + 3 + 6 + 4 = 13.

Actually, if you had one more bottle that you didn't feed to any rats, that would cover 0 rats dead.
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Re: Math Puzzles (Read the Rules!)

Postby NoLifeLeft » Thu Apr 15, 2010 10:32 am

Ah, crap... Gimme a minute. damn OP edits
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Re: Math Puzzles (just for Chuck)

Postby chiggins » Thu Apr 15, 2010 10:33 am

Timko wrote:Wine numbers in binary
1 - 0001
2 - 0010
3 - 0011
4 - 0100
5 - 0101
6 - 0110
7 - 0111
8 - 1000
9 - 1001
10 - 1010
11 - 1011
12 - 1100
13 - 1011


(Right, or you can do bit masks :) )
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Re: Math Puzzles (Read the Rules!)

Postby NoLifeLeft » Thu Apr 15, 2010 10:45 am

You need to boil eggs for exactly 9 minutes, or else the visiting Duchess will complain, and you will lose your job as head chef.

But you have only 2 Hourglasses, one measures 7-minutes, and the other measures 4-minutes. How can you correctly measure 9 minutes?
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