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Something to get your brains working
novacaine - 7/4/08 at 06:34 PM

ok, i was set this problem, i have thought of one solution but it relys on circumstances. lets see what you guys get




there are a group of 12 people who all weigh exactly the same

One person changes his weight, you dont know if he has put on weight or lost it.

you have a large set of balances that you can only use 3 times

you must identify the person who has changed their weight

good luck !!

Confused but excited. - 7/4/08 at 06:40 PM

I did this once with bags of sugar.
As for lifting people on and off scales at my time of life, well.........................

Davey D - 7/4/08 at 06:52 PM

Easy!

1) put 6 on either side of the scale.. discard everyone on the lighter side

2) put 3 people either side of the scale.. discard everyone on the lighter side

3) put 1 person on either side of the scales.
if it tips 1 way that person is the heaviest.. if they are balance the person you didnt put on the scales is the heaviest

what do a get for a prize

blakep82 - 7/4/08 at 07:00 PM

i'd just ask them personally.

eznfrank - 7/4/08 at 07:08 PM

Same as Davey D although if 1/2 or more of "the group" to which you originally refer are female you could even do it in two, as it is a "he" that has changed "his" weight?

eznfrank - 7/4/08 at 07:14 PM

Oh hang in a minute, we aint looking for heaviest are we, just weight change. Hmm.

matt_claydon - 7/4/08 at 07:18 PM

quote:
Originally posted by Davey D
Easy!

1) put 6 on either side of the scale.. discard everyone on the lighter side

2) put 3 people either side of the scale.. discard everyone on the lighter side

3) put 1 person on either side of the scales.
if it tips 1 way that person is the heaviest.. if they are balance the person you didnt put on the scales is the heaviest

what do a get for a prize


That doesn't work, as the person you are looking for might be in the light group.

Griffo - 7/4/08 at 07:19 PM

quote:
Originally posted by Davey D
Easy!

1) put 6 on either side of the scale.. discard everyone on the lighter side

2) put 3 people either side of the scale.. discard everyone on the lighter side

3) put 1 person on either side of the scales.
if it tips 1 way that person is the heaviest.. if they are balance the person you didnt put on the scales is the heaviest

what do a get for a prize


But that is assuming that the guy put on weight, if he lost weight you would have discarded him.






I think you split them into three groups of four. lets call them 1,2 and 3

firstly you weigh 1 vs 2

now there are three outcomes

easy outcome...the scales balance!
this means 3 is the odd one out.
lets call the four people in 3 mr a, b, x and y

you know weigh a vs b

then a vs x

if outcome is
a v b - a v x = balance = y is odd one out
a v b tips to a and a v x tips a then a is heavy
a v b tips to a and a v x balances then b is light

and so on until heavy/light person is found.





If '1' and '2' do not balance then either 1 or 2 is heavy or light.

at which point i am now stuck as unless you know which is heavy or which is light i can not see a way of determining which of 8 people it could be with only 2 measurments left



I really hope someone will come along and finish this of for me or get it right as im dying to know.


Edit: although if you where lucky enough to weigh people in one of the uneven groups and the scales not balance you could then use the above method, but as the person who posted this mentioned that relys on circumstance/luck.




How about leave a pie on the table and check to see who eats it

[Edited on 7/4/08 by Griffo]

matt_claydon - 7/4/08 at 07:33 PM

Griffo is on the right track. This is a very old puzzle and is usually quoted as finding a counterfeit coin from a selection of 12. It's not as trivial as it sounds but a google for "counterfeit 12 coins" should provide the answer

Griffo - 7/4/08 at 07:34 PM

but thats cheating!!!

JoelP - 7/4/08 at 08:47 PM

i just wrote a long rambling answer and realised that 3 groups isnt the way forward! So here goes with 4 groups of three!

Group A vs B, if they are the same discard both. You would then know that C and D were different. Or, if A and B were different, discard C and D. Either way drop the tags and you have used one step to get two groups of three people that are different total weights. Rename remaining groups A and B.

no point doing A vs B cos you wouldnt know which was light or heavy. Name people A1, A2, A3, B1, B2 and B3.

A1+A2 vs B1+B2, if they are the same, either A3 or B3 is the target, compare either to A1 to find him. This would be job done in three steps.

If not the same, take A3+B3 as your pair of normal people, and compare to A1+B1. This should provide a list of possible results and logical answers from each.


If a1a2 > b1b2 but a3b3>a1b1, then B1 is light

If a1a2 > b1b2 but a3b3<a1b1, then A1 is heavy

If a1a2 > b1b2 but a3b3=a1b1 then either a2 is heavy or b2 is light, which sadly fails the 3 steps. And i cant be arsed trying again!

Puk - 7/4/08 at 08:52 PM

This works but it does require a Chapman like approach to the rules, which surely on a Locost site must be ok

Split your 12 into 3 groups of 4, A, B & C

Scenario 1:
1st use of scale: Now load up groups A and B on the scale
If they balance then you know that our man is in group C.
2nd use of scale: Take 2 from group A and any 2 from group C
If they balance then our man is 1 of the 2 left from group C
3rd use of scale: Take 1 from group A and 1 of the 2 who are still to be weighed from group C
If they balance then it is the last guy who has not been weighed from group C
If they don’t then it is the guy from C who is on the scale. Sorted

Scenario 1b:
1st use of scale: as scenario 1 & same outcome – they balance and we know our man must be in group C
2nd use of scale: as scenario 1 but different outcome:
The scale didn’t balance, our man is one of the 2 that were added to the scale from group C
3rd use of scale: take one of the guys from each side of the scale.
If they now balance then it was then the guy from group C who just got off. If they don’t then it’s the guy from C who is still in the scale. Done

Scenario 2: Now it gets tricky.
1st use of scale: as scenario 1 but different outcome
The scale does not balance. So our man is not in group C. Get 2 guys to jump off each side of the scale and look to see if they balance. If they don’t its 1 of the 4 left on the scale (scenario 2a). If they do its 1 of the 4 who just jumped off (scenario 2b).

Scenario 2a:
2nd use of scale: Replace the 2 guys from group B with 2 fresh guys from group C (because you know that they are all of equal weight in group C).
Scenario 2a1:
If they balance it is one of the 2 guys from B who just got off.

3rd use of scale:
Take one of the guys that just got off and balance against a guy from group C.
If they balance it is the guy the guy from B that did not get back onto the scale. If they don’t it’s the guy from B that is still on the scale. Sorted

Scenario 2a2:
They didn’t balance, so it’s one of the 2 guys from group A that are still in the scales.
3rd use of scale:
Take one of the A guys out of the scale and balance against a guy from group C.
If they balance it is the guy the guy from A that just got of the scale. If they don’t it is the guy from A still on the scale. Done

Scenario 2b: Its 1 of the 4 guys that jumped of either side of the scale after the first use.
2nd use of scale: Take 2 of them and compare with 2 from C
If they balance it is 1 of the 2 that didn’t get put back in the scale. Scenario 2b1
If they don’t balance its 1 of the 2 that are in the scale (but it is not either of the ones from C): Scenario 2b2
3rd use of scale:
Scenario 2b1: Compare 1 of the 2 guys from the 1st balance that was asked to sit out the 2nd balance against a guy from C. If they balance then it is the other guy. If they don’t it’s the one in on the scale that isn’t from group C. DONE

Scenario 2b2: Take one guy of each side of the scale. If they balance it is the guy that just got off that wasn’t from C. If they don’t it’s the guy on the scale that isn’t from C. DONE

So this works if we allowed to read the scale as it is unloaded without that counting as a new use of the scale. Surely your honor!

Big Stu - 8/4/08 at 05:37 AM

quote:
Originally posted by Puk

So this works if we allowed to read the scale as it is unloaded without that counting as a new use of the scale. Surely your honor!


In that case put all 12 on the scales then take them off one at a time and see which one is different.

Puk - 8/4/08 at 07:49 AM

quote:
In that case put all 12 on the scales then take them off one at a time and see which one is different.


Fair point

02GF74 - 8/4/08 at 08:04 AM

quote:
In that case put all 12 on the scales then take them off one at a time and see which one is different.


except that you will have used the scales more than 3 times.

eznfrank - 8/4/08 at 09:19 AM

Put the scales on Ebay and with the ££ you get, buy a big chocolate cake. Either 11 fatties will eat it, leaving the one thinny, or 1 fatty will go eat it leaving 11 thinnies.

How very scientific.

JoelP - 8/4/08 at 05:25 PM

if you do google it its a bloody nightmare!

Puk - 8/4/08 at 05:28 PM

I take it that there is a more ingenious solution than the one I posted then!

Is Novocain going to come and mark our home work at some point?

iank - 8/4/08 at 07:06 PM

quote:
Originally posted by Puk
...
Is Novocain going to come and mark our home work at some point?


I suspect someone will

Jon Hazan - 8/4/08 at 11:19 PM

Ok heres my attempt...

The group needs to be divided into 3 groups of 4.

place 4 on each side of the scales

Unbalanced:
----if the scale is unbalanced we can assume that all of the 3rd group are of neutral weight (n).
----We now know that 4 (u) have the possibility of being underweight and 4 (o) overweight

----Now take 2 (u) and 3 (o) and place them together on one side place the 4 (n) and remaining (o) on the other. The 2 (u) should be kept to a side.
----Balanced:
--------The 2(u) should be compared against each other.
------------Whichever side rises is the person who changed (Lost) weight
----Unbalanced 2(u)3(o) down:
--------This means our person is overweight and 1 of the 3 (o)'s, all the otheres are now (n)
--------To find him we just need to place 1 (o) on each side and keep 1 (o) to the side.
-------------Whichever side drops is the person who has changed (Gained) weight, if niether fall the 3rd person has changed (Gained) weight.
----Unbalanced 2(u)3(o) up:
-------- This means our person is one of the 2 (u)'s or the (o) with the (n)'s. To find just put the (u)'s on the scales.
-------------Whichever side rises is the person who changed (Lost) weight, if niether rise then the 3rd person has changed (Gained) weight

Balanced (From the 4v4):
----All the people on the scales are now (n). Take the remaining 4 and put 2 on one side and 1 on the other with an (n). Keep the 4th unknown to a side.
----Balanced:
--------The unknown is the person who changed (Unknown) weight And can be tested against a neutral if change direction is needed.
----Unbalanced Pair down:
--------This means the 2 Unknown are (o) and the single Unknown is (u). Put the (u) to one side and as above compare the (o)'s.
------------Whichever side drops is the person who has changed (Gained) weight, if niether fall the 3rd person has changed (Lost) weight.
----Unbalanced Pair up:
--------This means the 2 Unknown are (u) and the single Unknown is (o). Put the (o) to one side and as above compare the (u)'s.
------------Whichever side drops is the person who has changed (Lost) weight, if niether fall the 3rd person has changed (Gained)


This is a complete answer i think but please check it!! It gives both the person required and the weight change direction

Got anymore puzzles?

Edit: Corrected some bb coding

[Edited on 8/4/08 by Jon Hazan]

Puk - 9/4/08 at 04:53 AM

By jingo - I think you've cracked it!