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be_water

Posts: 70
Registered: Feb 23, 2011
Tough Puzzle
Posted: Jul 31, 2015, 3:41 AM

I was recently watching a TV show (Brooklyn 99) where they mentioned a brain teaser that was supposed to be impossibly tough. It took me a few hours to figure it out (The hopping in the shower to think clearer trick worked for me). I really enjoyed it so I thought I would share it with you guys.



Here it is:

You have 12 marbles. 11 of the marbles weigh exactly the same. We do not know if the 12th marble weighs more or less but we know it doesn't weigh the same. Using a balance scale only 3 times find the one odd marble out.




Hope you guys enjoy it. If someone else has a similar type of tough puzzle I would love to hear it; so go ahead and post it. If there is interest in this type of stuff I have another puzzle that comes to mind I could post. It was on an application for a math summer camp and it took me days to figure out.



be_water

Posts: 70
Registered: Feb 23, 2011
Re: Tough Puzzle
Posted: Jul 31, 2015, 4:06 AM

Also interesting questions that would go along with that puzzle after you figure it out are:


How many marbles could I sort through with 4 uses of the scale? How about 5?

How many uses would I need for some huge number of marbles like a billion?

number42

Posts: 6
Registered: Jun 2, 2015
Re: Tough Puzzle
Posted: Jul 31, 2015, 10:08 AM

Hi Be_water,

sorry but I figured that out in 2 mins! :-|

I will post my answer to you directly.

42

rainwolf

Posts: 676
Registered: Apr 12, 2008
From: Singapore
Age: 40
Home page
Re: Tough Puzzle
Posted: Jul 31, 2015, 10:44 AM

Nice number42, I heard the riddle about 18years ago and it took me a couple of weeks back then.

There's an extension to it, namely to prove (via induction) that you can do the same using the balance n times for 4x3^(n-2) marbles.

\_(ツ)_/
zappazappa

Posts: 7
Registered: Jan 8, 2014
Re: Tough Puzzle
Posted: Aug 3, 2015, 3:27 AM

Do you know this one?

three gods , A, B and C, are called "True", "False", and "Random". "True" always tells the truth , "False" always tell falsehoods, and what "Random" says is completely random (randomly, can be true or false). Your task is to determine the identities of A, B and C by asking three questions that they will answer "yes" or "no" ; each question has to be made to exactly one god. The gods can understand english, but will respond to all questions in their own language, in which, the words for "yes" and "no" are "da" and "ja". You do not know what word means what.


Message was edited by: zappazappa at Aug 3, 2015 8:54 AM


number42

Posts: 6
Registered: Jun 2, 2015
Re: Tough Puzzle
Posted: Aug 3, 2015, 9:35 AM

Hi Zappa,

I have since spent some time working on the three Gods puzzle. I stand corrected. This is much harder than I realized! I worked out that a more complicate boolean construction is needed in each step but haven't the time to work it out, so I cheated by looking it up in wikipedia :-|. That is one tricky puzzle.

I have one for you though...

On an island there are 30 lizards.
6 Greens
10 Blues
and 14 Reds

When they mate in different combinations of colors the lizards don't reproduce but simply change color. This happens according to the following rules:

Red mates with Red they Change to one Blue and one Green
Blue mates with Blue they change to one Red and one Green
Green mates with Green they change to one Blue and one Red

And
Blue mates with red gives two Greens
Green mates with Red gives two Blues
Green mates with Blue gives two Reds

Your problem is:
Starting with 6 Greens, 10 Blues and 14 Reds, can you use these rules to end up with 10 of each color?
You must provide a proof with your answer.


Message was edited by: number42 at Aug 11, 2015 7:01 AM


Message was edited by: number42 at Aug 25, 2015 2:47 AM


number42

Posts: 6
Registered: Jun 2, 2015
Re: Tough Puzzle
Posted: Aug 5, 2015, 3:09 AM

hi Rainwolf,

I forgot to reply to your part about proving by induction that the solution applies to 4 x 3^(n-2). Yes, this seems intuitively obvious since the unweighed set in each step also scales to the same value minus one. Eg. The unweighed set scales at 4 x 3^(n-3).

I hope this makes sense. I have been deliberately obscure so as not to give the solution to others who might want to attempt it.

kolia

Posts: 28
Registered: Mar 22, 2008
From: Cambridge, England
Age: 27
Re: Tough Puzzle
Posted: Aug 22, 2015, 5:22 PM

Marbles puzzle is a good one. I was asked about it (8 marbles, 1 heavier) on a job interview. You are expected to provide the correct answer in a minute.

Back at uni I wrote an article about 3 gods puzzle. I think my explanation took 2 pages. It's definitely a hard one and it requires some time to think it through.

Few other puzzles I was asked about:
- How would you count people in the crowd? The trick is to come up with an efficient method (and there is one!).
- There are 25 horses. The goal is to select the 3 fastest in the group. In a single race only 5 horses can run. Find the minimum # of races you need to organize in order to find the top 3. You are not allowed to use stopwatch.
- You have a 100 step ladder and 2 eggs. An egg can be dropped from any step, and it will either break or not. Your goal is to find in an efficient way the highest step from which an egg can be dropped without breaking. If you dropped an egg and it didn't break you're allowed to reuse it. In the process you are allowed to break both eggs.

Enjoy.

rainwolf

Posts: 676
Registered: Apr 12, 2008
From: Singapore
Age: 40
Home page
Re: Tough Puzzle
Posted: Aug 23, 2015, 7:11 PM

Hey Kolia, your marbles puzzle sounds different from mine. I've heard a similar one before:
There are 9 jars with an unlimited supply of marbles in each. 8 jars contain marbles which weigh 1gr each, and one jar contains marbles which weigh 1.1gr each. You also have an electronic scale which is accurate up to a 10th of a gram. Use the scale exactly once to determine which jar contained the odd (1.1gr) marbles.

\_(ツ)_/
kolia

Posts: 28
Registered: Mar 22, 2008
From: Cambridge, England
Age: 27
Re: Tough Puzzle
Posted: Aug 23, 2015, 11:26 PM

Heard it.

If people are interested in mathematical puzzles, it's worth checking Martin Gardner. He was a quite prolific mathematician who had a column in Scientific American about games. I think most of his articles were later turned into books. I had one at home when I was a kid. At the time I found them pretty challenging.

I remembered one more puzzle. I was very pleased when I arrived with the right solution (admittedly, it took me a while) and wanted to trick my friend. So, I asked him about it on our way from the pub. It was quite devastating for my ego, because he gave me the correct answer in about 10-15 seconds, despite the fact being a bit tipsy.

Anyway, the puzzle goes like this. Put 10 trees on 5 lines, each containing 4 trees.

zoeyk

Posts: 1,964
Registered: Mar 4, 2007
From: San Francisco
Age: 41
Home page
Re: Tough Puzzle
Posted: Aug 24, 2015, 2:33 AM

ɹɐʇs ɐ

45 seconds.

Scire hostis animum - Intelligere ludum - Nosce te ipsum - Prima moventur conciliat - Nolite errare
number42

Posts: 6
Registered: Jun 2, 2015
Re: Tough Puzzle
Posted: Aug 24, 2015, 6:17 AM

sorry zoeyk, I got it in about 3 seconds. It was an intuitive guess, but I got it right, without even having to be drunk.

number42

Posts: 6
Registered: Jun 2, 2015
Re: Tough Puzzle
Posted: Aug 24, 2015, 6:19 AM

I note that no-one has responded to my lizard problem...

kolia

Posts: 28
Registered: Mar 22, 2008
From: Cambridge, England
Age: 27
Re: Tough Puzzle
Posted: Aug 24, 2015, 9:42 PM

Well done, very impressive.

number42

Posts: 6
Registered: Jun 2, 2015
Re: Tough Puzzle
Posted: Aug 25, 2015, 2:50 AM

Sorry, but I wrote out the rules for the lizard puzzle incorrectly. Please check my original post above for the now edited version.

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