OT - Interesting Mind Teaser
 

Ok, my friend sprung me on this tonight when (a) I was already semi-drunk (on the way to being fully drunk), and (b) without a pen and pad in front of me to help figure it out. He works with some Stat PhDs who decided to use this quesiton when interviewing other Stat PhDs who they were thinking of hiring.

I love these mind teaser things, kind of like an LSAT Logic Game type of thing (on steroids), so I couldn't get it off my mind (I was sitting at the SF Giants vs. Atlanta Braves game using my fingers to try and figure it out). I finally got if after a few innings and about 7 incorrect answers. If you know it already, keep quiet - no posting the answer to make you look smart if you've had prior help. If not, enjoy (if you like these sort of things)...

...You have 12 stones. 1 of the 12 weighs more or less than the other 12. You have to figure out which one it is, and whether it weighs more or less. How to figure this out? You have a balancing scale, and can only use it 3 times. How do you get the above task done?

Re: OT - Interesting Mind Teaser
 

[ QUOTE ]
Ok, my friend sprung me on this tonight when (a) I was already semi-drunk (on the way to being fully drunk), and (b) without a pen and pad in front of me to help figure it out. He works with some Stat PhDs who decided to use this quesiton when interviewing other Stat PhDs who they were thinking of hiring.

I love these mind teaser things, kind of like an LSAT Logic Game type of thing (on steroids), so I couldn't get it off my mind (I was sitting at the SF Giants vs. Atlanta Braves game using my fingers to try and figure it out). I finally got if after a few innings and about 7 incorrect answers. If you know it already, keep quiet - no posting the answer to make you look smart if you've had prior help. If not, enjoy (if you like these sort of things)...

...You have 12 stones. 1 of the 12 weighs more or less than the other 12. You have to figure out which one it is, and whether it weighs more or less. How to figure this out? You have a balancing scale, and can only use it 3 times. How do you get the above task done?

[/ QUOTE ]

I saw this once, and it's a huge pain in the ass, with one of the cases about three pages long. The obvious solutions don't work.

Re: OT - Interesting Mind Teaser
 

[ QUOTE ]
I saw this once, and it's a huge pain in the ass, with one of the cases about three pages long. The obvious solutions don't work.

[/ QUOTE ]

The jist is simpler than that, it might take a long time to explain every scenario, but that main key is a bit of a twist that doesn't jump out right away (though what it accomplishes logically can be explained succinctly).

Re: OT - Interesting Mind Teaser
 

This is gonna kill me.

Re: OT - Interesting Mind Teaser
 

So tired, but I'll try. Break the stones into 3 groups of 4. Weigh 2 of the groups. If they weigh the same, you know the stone is in the 3rd group.

If they weigh the same(call them 1, 2, 3, so if 1=2) put 2 stones from 3 on one side(call them 3a and 3b) and one stone from 3(3c) and one stone from 1 on the other side. If they are equal again, the 4th stone from group 3 is the different one. Weigh it against a stone from group 1.

If the side with the stone from 1 is heavier, either 3c is heavy or one of 3a or 3b is light. Weigh 3a and 3b. If they are equal, 3c is the heavy stone. If they aren't equal, the lighter of the two is the light stone.

If the side with 2 stones from 3 is heavier, either 3c is light or one of 3a or 3b is heavy. Weight 3a and 3b. If they are equal, 3c is the light stone. If they aren't equal, the heavier one is the heavy stone.

Uh, if 1|=2, I dunno. Takes more thought.

Re: OT - Interesting Mind Teaser
 

After a whopping minute or two, I have no [censored] idea what do if the different one is in 1 or 2. You only have 2 weighings left. You know 7 of them are normal, and you know where 4 normal stones are. I suspect it involves swapping in some known normal stones, but how many and to what side escapes my feeble intellect.

Re: OT - Interesting Mind Teaser
 

[ QUOTE ]
I suspect it involves swapping in some known normal stones

[/ QUOTE ]

You are wiser than you think young grasshopper...

...It's bad enough to tackle the problem drunk with time on your hands, tired and about to go to bed is worse I think...

Re: OT - Interesting Mind Teaser
 

[ QUOTE ]
[ QUOTE ]
I suspect it involves swapping in some known normal stones

[/ QUOTE ]

You are wiser than you think young grasshopper...

...It's bad enough to tackle the problem drunk with time on your hands, tired and about to go to bed is worse I think...

[/ QUOTE ]

At least you're not trying to tackle it with Yugo yelling in your ear after he's just beaten you HU.

Re: OT - Interesting Mind Teaser
 

Alright, I tried to go to bed and this [censored] kept me up but I think I got it.

Same notation as above, if 1<2, either one of group 1 is light or one of group 2 is heavy. Take 1d and 2d and place them off the scale. The lighter initial side will have 1a, 1b, 2a, and 2b on it. The heavier side will have 2c, 1c, 3a, and 3b on it. 1d and 2d you remove. Reweigh. If they are equal, weigh 1d against a 3. If it is equal, 2d is heavy, if not it is light.

If the heavier initial side is now lighter, one of the balls that changed position(either 2a, 2b, or 1c) is the different one. Weigh 2a vs 2b. If they are equal 1c is light. If they aren't, the heavier one is the heavy. If the heavier initial side is still heavy, either 1a, 1b, or 2c is the different one. Weigh 1a and 1b against each other as above but reversed. You can also reverse the whole thing if 1>2 initially. And yeah, my notation system was a bad idea but it would be too confusing to change now.

Re: OT - Interesting Mind Teaser
 

second: 2a 2b 1a - 2c 2d 1b

if same: 1c or 1d is light.
third 1c - 1d, light one goes up.

if left side heavy: 2a or 2b is heavy or 1b is light.
third 2a - 2b.
if equal 1b is light, otherwice the heavy of 2a and 2b goes down.

Re: OT - Interesting Mind Teaser
 

Definitely does not take 3 pages.

I solved this a few years back. I came up with a tricky solution and thinking about it years later came up with a more simple, almost elegant solution.

Great puzzle, it took me a while.

Re: OT - Interesting Mind Teaser
 

Just wanted to add that if you solved this in a mere couple of innings then you are a much better man than I (though I guess I knew this already).

Me personally, a friend at work gave me this to chew on, I spent an hour or 2 at work mulling it over when I had a chance, thought about it on the way home from work, another 45 minutes or so, thought about it when falling asleep at night, another half hour or so, let my subconcsious work on it while sleeping and then on the way to work the next day it finally came to me.

I enjoy thinking about stuff like this. If you (or anyone else) has more logic problems like this I would love to hear them. So far this particular one is my favorite.

I will also add that I have presented this problem to several people, so far noone has solved it so it's not all that easy though I suspect several were capable of doing so but they have lives to live unlike me I suppose. I really should get a life. Sigh.

Re: OT - Interesting Mind Teaser
 

Here is a fun one.

RiverIQGame
and then click the BLUE CIRCLE to start the game.

Here are the rules -
Everybody has to cross the river.
Only two persons on the raft at a time.
The father cannot stay with any of the daughters without their mother's presence.
The mother cannot stay with any of the sons without their father's presence.
The thief (striped shirt) cannot stay with any family member if the policeman is not there.
Only the father, the mother and the policeman know how to operate the raft.

To start, click on the big blue circle on the right.

To move the people, click on them.

To move the raft, click on the pole on the opposite side of the river.

~Teck

Re: OT - Interesting Mind Teaser
 

Is it too easy?!

Step 1: Separate in 2 groups of 6. Use scale.. Take the group that weights more.

Step 2: Separate remaining 6 in 2 groups of 3. Use Scale, take the group that weights more

Step 3: Take 2 of the 3 left. Use scale. If they are equal, it means the last stone you didn't weight is the one. If the stones aren't the same, you found out witch one it is!

Edit: Oups.. I guess it doesn't work since we don't know if it's more or less [img]/images/graemlins/wink.gif[/img]... But the solution is easy tought

Re: OT - Interesting Mind Teaser
 

yeah but when you weigh the 2 out of 3 left on last turn you will find they are the same or that one is more than the other, if you get the same you dont know if the one you did not weigh is more or less than the other two and if you get that they weigh different you dont know which one weighs different then the one you didnt weigh.

Re: OT - Interesting Mind Teaser
 

Pretty damn easy...

1) Break 12 into three groups of four.

1234 5678 90ab

b) Weight group 1 vs group 2
1234 vs 5678

c) if same, weight group 90ab has the bad one.

ci) 34 vs 90 -> 34 is normal, find if 90 is off. if it weighs the same, ab has abnormal one, and just weigh 1 vs a.

cii) if it weighs different, 90 has the bad one, weight 1 vs 9

d) if different, culprit is within these two groups. 90ab has all normal balls. note which side is heavier.

di) 9012 vs 3456. If they weigh the same, then culprit is either 7 or 8.

dii) if 9012 weighs more, and 1234 was heavier, then 1 or 2 is heavier than the rest.

diii) if 9012 weighs more, and 5678 was heavier, then 3 or 4 was the heavier culprit.

and so on. its a little tricky, but you can get it a lot easier if you actually try it out with 12 balls.

Re: OT - Interesting Mind Teaser
 

Wrong. For example:

dii) if 9012 weighs more, and 1234 was heavier, then 1 or 2 is heavier than the rest. .. OR 5678 contains one that is lighter.

Re: OT - Interesting Mind Teaser
 

That was really fun!

Thanks.

Re: OT - Interesting Mind Teaser
 

Fun puzzle! Answer below

<font color="white">
1) two groups, 1234 and 5678, with 90AB off the scale

2) If they balance, compare 123 with 90A
2a) If those balance, then
2ai) B is the fake coin, compare it to a good coin to determine heavier or lighter
2b) If the don't balance
2bi) then we know that if 123 is heavier then the coin is light and in 90A, and if it's lighter then the coin is heavy (and in 90A)
2bii) Weigh 9 vs. 0. If the coin was determined to be heavy in 2b heavy then the heavier coin is the fake, otherwise the light one is
2biii) Otherwise A is the fake with heaviness determined in step 2b

3) If the left side went down, compare 1678 with 5OAB
3a) If they balance
3ai) then we know that the bad coin is in the group 234 and is light. So weight 2 vs 3 and the lighter is the fake, if they balance then 4 is the fake (and is light)
3b) If the left side goes down again, then we know for sure that either 1 is heavy or 5 is light (and 9 is of course real). So weigh 1 vs. 9, if 1 is heavy then that's the fake, if they balance then 5 is the fake and it's light.
3c) If the right side now goes down, then we know that the fake moved from one side to the other (which means it's in group 678) and is light.
3ci) Use the procedure from 2bii to determine which the fake coin is

4) If the right side went down, we can compare 1678 with 5OAB here also
4a) The solution is symetrical, just replace all "light" with "heavy" and vice versa.
</font>

Re: OT - Interesting Mind Teaser
 

[ QUOTE ]
Wrong. For example:

dii) if 9012 weighs more, and 1234 was heavier, then 1 or 2 is heavier than the rest. .. OR 5678 contains one that is lighter.

[/ QUOTE ]

Yeah, it's the heavier or lighter part that is the tricky part.

Re: OT - Interesting Mind Teaser
 

[ QUOTE ]
Me personally, a friend at work gave me this to chew on, I spent an hour or 2 at work mulling it over when I had a chance, thought about it on the way home from work, another 45 minutes or so, thought about it when falling asleep at night, another half hour or so, let my subconcsious work on it while sleeping and then on the way to work the next day it finally came to me.


[/ QUOTE ]

Me too - sometimes I can't get this kind of sh-t out of my head until I think I have it figured out...

Hints (smallish)
 

Within your first two weighings, you can narrow the irregular stone down a group of 3 stones or less, and know whether the irregular one is too light or too heavy. Once you get to that point, it's easy to figure out which stone it is on the 3rd weighing.

That, and the first weighing is 4 vs. 4 (because of the fact that you don't know if the irregular stone is lighter or heavier, going 6 vs. 6 gives you zero information, etc.).

I'll try and post an easy-to-read answer later this afternoon (someone may have posted the correct answer, but I'm hungover and it's hard to tell).

Re: OT - Interesting Mind Teaser
 

Comment in white:

<font color="white"> Yeah, your step when the two sets of 4 balance is the trick. How to rearrange the stones on the 2nd weighing so that you narrow it down to a group of 3 (or 2), and know whether it's heavier or lighter is the key. Taking 3 normal stones and switching them with 3 from one side, then "flipping" that 4th stone with one from the other side is what took me so damn long to figure out on this one (You've already narrowed it down to 8, that splits it up into groups of 2, 3, and 3 and lets you know which group it's in, and whether it's too heavy/too light). That's the funky step that gives you the requisite information to figure out the rest with just one more weighing.</font>

Re: OT - Interesting Mind Teaser
 

I haven't read a single post yet, but, can I rub a magic genei and get one more use on the scale? I'm still working on this... (and not looking).

Re: OT - Interesting Mind Teaser
 

Misread question .... rigged.

Re: OT - Interesting Mind Teaser
 

Ok, I'm going to start with the lucky route first (again, I haven't read a single subpost yet).

Measurement 1:
Split into 3 sets of 4 rocks. Weigh two sets against each other. If you are lucky, they will be even, thus indicating that the "odd" rock is one of the 4 remaining rocks.

Measurement 2:
Choose any two rocks and weigh. If you're lucky they will not be even, and you'll have figured out which one of two it is. Keep the rock that is heavier, and weigh it against any of the other rocks.

Measurement 3:
If the heavier rock is even with the last measurement, you'll know the "odd" rock is the one not measured here, and it is lighter than the rest.
Edit: I should add if this last measurement is not even, the "odd" rock is heavier.

Ok, now I have to figure out how to do this if Measurement one is not even. [img]/images/graemlins/tongue.gif[/img] (still not reading)

Re: OT - Interesting Mind Teaser
 

I hate this problem. It ruined a perfectly good night out with friends for me once.

Re: OT - Interesting Mind Teaser
 

this may be the most -ev post I've read since the damn paper throwing game post. thanks gramps......

Re: OT - Interesting Mind Teaser
 

I think I got it.

Should I post it?

Re: OT - Interesting Mind Teaser
 

[ QUOTE ]
I think I got it.

Should I post it?

[/ QUOTE ]

I think durron posted it about as succinctly as you can (and in white so as not to give it away if people don't want to see it...)

Re: OT - Interesting Mind Teaser
 

Don't read this if you are still trying.
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+
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<font color="white">
you devide stones into two groups - 6 and 6.. plop them on the scale - whichever side drops your stone is in that 6

we do it again.. 3 and 3 - same result

we are now down to 3 stones (one of which is our heavy stone)

we put any random 2 on the scale (1 on each side)

if we put both on the scale and it is even (scale doesnt drop either way)- they are both light and the one we didnt put on the scale is our stone.

if one side drops.. that is our stone.

- ClockWyze </font>

Re: OT - Interesting Mind Teaser
 

You don't know if the stone is heavy or light ClockWyze

Re: OT - Interesting Mind Teaser
 

You don't know if the irregular stone is lighter or heavier. Weighing 6 vs. 6 gives you zero information - you don't know if one side contains a heavier stone, or the other contains a lighter stone...

Re: OT - Interesting Mind Teaser
 

Durron- I'm sorry, I was too tired to think about spoilers when I was thinking about this last night. Can you edit my posts into whiteness?

my solution - a little more elegant I believe
 

Durron's answer was perfect, well done.

Here's another way to skin the cat, if 4 on 4 doesn't balance then for the second step do this:

I will label the balls like this at this point -

4E
4H
4L

E - even (the ones that were off the scale in step 1 and are therefore fine)
H - even or maybe heavy
L - even or maybe light

I just find this a little easier to follow then 123456...


Put on the scales 2H and 1L on each side.

If they balance then it's one of 2L that are off the scale ... easy.
If they don't balance then you've narrowed it down to 2H from the side that was heavier and 1L from the other side, weigh the 2H heads up against each other, if they balance it's the L, if not then the heavier side is it.


When I first solved this my second step was to weigh 3H and 2L against 1H and 4E. That worked of course but my new solution is cleaner.

Cheers.

Re: OT - Interesting Mind Teaser
 

I think I have it, does it involve dividing the group of 12 into four different groups of 3?

Re: OT - Interesting Mind Teaser
 

LOL.

I remember that one, fortunately I didn't lose more than maybe half an hour of life on that one.

How bad was it for you lacky? I think the OP on that one had some totally absurd amount of consecutive hits that I can't even imagine approaching. I remember thinking that there was wind blowing like on a golf course or something,you never could tell where the damn paper was gonna go.

Re: OT - Interesting Mind Teaser
 

[ QUOTE ]
I think I have it, does it involve dividing the group of 12 into four different groups of 3?

[/ QUOTE ]

Sort of. To summarize my solution into one sentence, <font color="white"> you divide them into three groups of 4 with the first weighing, (1234, 5678, 90AB), and then 4 groups of 3 (234, 678, OAB, 159), and then use the last weighing to solve the last group of 3.</font>

Re: my solution - a little more elegant I believe
 

[ QUOTE ]
Durron's answer was perfect, well done.

Here's another way to skin the cat, if 4 on 4 doesn't balance then for the second step do this:

I will label the balls like this at this point -

4E
4H
4L

E - even (the ones that were off the scale in step 1 and are therefore fine)
H - even or maybe heavy
L - even or maybe light

I just find this a little easier to follow then 123456...


Put on the scales 2H and 1L on each side.

If they balance then it's one of 2L that are off the scale ... easy.
If they don't balance then you've narrowed it down to 2H from the side that was heavier and 1L from the other side, weigh the 2H heads up against each other, if they balance it's the L, if not then the heavier side is it.


When I first solved this my second step was to weigh 3H and 2L against 1H and 4E. That worked of course but my new solution is cleaner.

[/ QUOTE ]

Yeah, that (the 3 vs. 3 on the 2nd step, etc.) looks even cleaner than durron's answer (which was the one I came with). Call it "mind teaser FPS" on our part....

Re: OT - Interesting Mind Teaser
 

eh, only played an hour maybe. I have far better games sitting around not being played. It was chalanging though