## Math Puzzles (Read the Rules!)

Non-Disc Golf Stuff

Moderators: Timko, Fritz, Solty, Booter, Blake_T, Frank Delicious

### Math Puzzles (Read the Rules!)

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.
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?
jsun3thousand wrote:Disc golfers are holding the sport back.
Timko
Like Angels Kicking Ass in your Mouth

Posts: 7708
Joined: Wed Aug 02, 2006 10:21 pm
Location: KCMO

### Re: Math Puzzles (just for Chuck)

"The Gauge may be the best disc ever"
-dgdave

Destroyer/Enforcer/PD/TD/Escape/XXX/Gauge/Suspect/P1x/P2
dgdave
DGR Postmaster General

Posts: 12111
Joined: Mon Jan 15, 2007 8:22 pm
Location: Central OK
Favorite Disc: GAUGE!

### Re: Math Puzzles (just for Chuck)

Can I?
Tern | Jackal - Hatchet - Resistor | Truth - Theory | Clutch - Harp
Monocacy
Fairway Surgeon

Posts: 552
Joined: Mon Dec 21, 2009 4:05 pm
Location: Maryland
Favorite Disc: Clutch

### Re: Math Puzzles (just for Chuck)

Of course. Just remember, SHOW YOUR WORK! Math is a process, not an answer.
jsun3thousand wrote:Disc golfers are holding the sport back.
Timko
Like Angels Kicking Ass in your Mouth

Posts: 7708
Joined: Wed Aug 02, 2006 10:21 pm
Location: KCMO

### Re: Math Puzzles (just for Chuck)

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.
"The Gauge may be the best disc ever"
-dgdave

Destroyer/Enforcer/PD/TD/Escape/XXX/Gauge/Suspect/P1x/P2
dgdave
DGR Postmaster General

Posts: 12111
Joined: Mon Jan 15, 2007 8:22 pm
Location: Central OK
Favorite Disc: GAUGE!

### Re: Math Puzzles (just for Chuck)

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.
NoLifeLeft
1000 Rated Poster

Posts: 1668
Joined: Sat Feb 03, 2007 10:13 pm
Location: Winchester, VA
Favorite Disc: a whole bag of 'em

### Re: Math Puzzles (just for Chuck)

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?
Disc Whore

Posts: 3459
Joined: Wed Jun 02, 2004 11:37 am
Location: Urbandale, IA

### Re: Math Puzzles (just for Chuck)

Updated the description. Sorry; I only saw this one in passing when talking with a teammate.
jsun3thousand wrote:Disc golfers are holding the sport back.
Timko
Like Angels Kicking Ass in your Mouth

Posts: 7708
Joined: Wed Aug 02, 2006 10:21 pm
Location: KCMO

### Re: Math Puzzles (just for Chuck)

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

Fixed prior post for new description.
NoLifeLeft
1000 Rated Poster

Posts: 1668
Joined: Sat Feb 03, 2007 10:13 pm
Location: Winchester, VA
Favorite Disc: a whole bag of 'em

### Re: Math Puzzles (just for Chuck)

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.
jsun3thousand wrote:Disc golfers are holding the sport back.
Timko
Like Angels Kicking Ass in your Mouth

Posts: 7708
Joined: Wed Aug 02, 2006 10:21 pm
Location: KCMO

### Re: Math Puzzles (Read the Rules!)

NoLifeLeft, the ball is in your court.
jsun3thousand wrote:Disc golfers are holding the sport back.
Timko
Like Angels Kicking Ass in your Mouth

Posts: 7708
Joined: Wed Aug 02, 2006 10:21 pm
Location: KCMO

### Re: Math Puzzles (Read the Rules!)

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.
chiggins
2009 DGR Donator

Posts: 751
Joined: Mon Apr 27, 2009 8:51 am

### Re: Math Puzzles (Read the Rules!)

Ah, crap... Gimme a minute. damn OP edits
NoLifeLeft
1000 Rated Poster

Posts: 1668
Joined: Sat Feb 03, 2007 10:13 pm
Location: Winchester, VA
Favorite Disc: a whole bag of 'em

### Re: Math Puzzles (just for Chuck)

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 )
chiggins
2009 DGR Donator

Posts: 751
Joined: Mon Apr 27, 2009 8:51 am

### Re: Math Puzzles (Read the Rules!)

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?
NoLifeLeft
1000 Rated Poster

Posts: 1668
Joined: Sat Feb 03, 2007 10:13 pm
Location: Winchester, VA
Favorite Disc: a whole bag of 'em

Next