a puzzle i need help with?
 

Mate has just set me a puzzle which he has been set by someone else & i couldn't see an obvious answer straight away so just thought i'd ask on here if anyone has come across it &/or knows the answer before i try racking my brain if it's not possible of sumin....;)
Anyway it goes like this:

you have 12 identical looking metal balls (bearings wotever). 11 are exactly the same weight & the 12th isn't maybe lighter or heavier.
You have a set of scales. You can use them 3 times with any combination of the balls on them at any time.
After the 3 uses of scales you have to distinguish which ball is different & whether it's heavier or lighter than the others. HOW?

Any cunning plans/solutions folks?
Ta
Si

GOT IT!!

You take the 12 balls and split them into 2 giving 6 each!!

Put the 2 groups of six on the scales!! whichever is heaviest keep and discard the other 6

Now your left with 6!! split into 2 groups giving 3 each group!!

Put the 2 groups on the scales! whichever is heaviest keep, discard the other group!!

You are now left with 3 balls

Split into 3! put 1 on each side of the scales and keep 1 to one side!

If your scales are eqaul then the ball you put to the side is heavier/lighter

But i cant flippen figure out how to distinguish which!

Anyone help??

put any two of the three balls on the scales.

if the scales balance you have the heaviest ball in your hand.

if the scales don't balance then...:)

cool

But you need to know whether its heavier or lightier so my theory is completly wrong!!

Need to start again

Weigh 1, 2, 3, 4 vs 5, 6, 7, 8 with 3 possible outcomes:-

1/ If they balance then 9,10,11,12 have the odd ball, so weigh 6,7,8 vs 9,10,11 with 3 possible outcomes:-
i/ If 6,7,8 vs 9,10,11 balances, 12 is the odd ball. Weigh it against any other ball to determine if heavy or light.
ii/ If 9,10,11 is heavy then they contain a heavy ball. Weigh 9 vs 10, if balanced then 11 is the odd heavy ball, else the heavier of 9 or 10 is the odd heavy ball.
iii/ If 9,10,11 is light then they contain a light ball. Weigh 9 vs 10, if balanced then 11 is the odd light ball, else the lighter of 9 or 10 is the odd light ball.

2/ If 5,6,7,8 > 1,2,3,4 then either 5,6,7,8 contains a heavy ball or 1,2,3,4 contains a light ball so weigh 1,2,5 vs 3,6,12 with 3 possible outcomes:-
i/ If 1,2,5 vs 3,6,12 balances, then either 4 is the odd light ball or 7 or 8 is the odd heavy ball. Weigh 7 vs 8, if they balance then 4 is the odd light ball, or the heaviest of 7 vs 8 is the odd heavy ball.
ii/ If 3,6,12 is heavy then either 6 is the odd heavy ball or 1 or 2 is the odd light ball. Weigh 1 vs 2, if balanced then 6 is the odd heavy ball, or the lighest of 1 vs 2 is the odd light ball.
iii/ If 3,6,12 is light then either 3 is light or 5 is heavy. Weigh 3 against any other ball, if balanced then 5 is the odd heavy ball else 3 is the odd light ball.

3/ If 1,2,3,4 > 5,6,7,8 then either 1,2,3,4 contains a heavy ball or 5,6,7,8 contains a light ball so weigh 5,6,1 vs 7,2,12 with 3 possible outcomes:-
i/ If 5,6,1 vs 7,2,12 balances, then either 8 is the odd light ball or 3 or 4 is the odd heavy ball. Weigh 3 vs 4, if they balance then 8 is the odd light ball, or the heaviest of 3 vs 4 is the odd heavy ball.
ii/ If 7,2,12 is heavy then either 2 is the odd heavy ball or 5 or 6 is the odd light ball. Weigh 5 vs 6, if balanced then 2 is the odd heavy ball, or the lighest of 5 vs 6 is the odd light ball.

iii/ If 7,2,12 is light then either 7 is light or 1 is heavy. Weigh 7 against any other ball, if balanced then 1 is the odd heavy ball else 7 is the odd light ball.

bollocks,

1 - 6 in each.
2 - 3 in each.
3 - 1 in each.

muppet:)

spoke too soon...I missed the "lighter bit":o

LOL

PMSL that's nothing i was thinking in new money where it's a set of scales which just tells you weight of wots on it rather than the balancing variety, doh explains why i was thinking it maybe impossible ;) lmfao
Si

You will know if heavier or lighter when you first weigh the 6 balls against the other 6 balls, then split as mentioned above

Nick

that wouldnt work thou as you would only know one set of 6 was lighter or heavier than the other you wouldn't be able to know which group contained the odd ball & thus you would know nothing about any specific set of balls & thus not be able to eliminate down to 1 in 2 more usages so WWSD's description is the only way i can see as such, where did you get it from? ;)
Si

STFI is what I did ;)

eeew thats a new un on me hang on i think i can solve it erm ahh "search the f3kin internet"? :eek: pmsl
Si

Owned (nearly) :D

...forget ye old fashioned balancing scales.....


pick 6 random balls and weigh them.

multiply the figure by 2, then divide by 12, you now have the weight of the average ball across the two packs of 6, assuming all balls weigh the same.

say the balls are "100g" each.


back to reading on the scales....................


650g + , you have the odd ball and it's heavier.

less than 550g you have the odd ball and its lighter.

You *should* not get a weight inbetween 550 and 650, it ill either be above or below.


2 more goes on the scales............:eek:


..lets say your fist weigh said 537, so we assume its got the lightweight oddball.....[mj's theory of weighabilty] the mid point of 12x100g average balls is 600g, the difference +/- of this figure will be the weight of the oddball multiplied by 2, thusly :rolleyes: the oddball is (600-537)x2=126g for the oddball.[/mj's theory of weighabilty]

pick 3 random balls and weigh them.

multiply the figure by 2, then divide by 6, you now have the weight of the average ball across the two packs of 3.

back to reading on the scales....



350g + , you have the odd ball and it's heavier.

less than 250g you have the odd ball and its lighter.

You *should* not get a weight inbetween 250g and 350g, it ill either be above or below.


1 more go on the scales...:eek:x2:

..You have 3 balls (ET) ;) ).





...over to you puzzle solvers, I'm too pissed. :)

is this not just a trick question ??? Why don't you pick each ball up in turn and you'll feel the heavier / lighter ball. Where does it say you HAVE to use the scales ???

Ignore my last post..the answer to the question is that it can't be done. :(

I ask you!!
 

Throw the scales in the bin and just look at the weights stamped on the fúckers.

F1!!! I think you just got it!! Take my method from earlier on! Find the odd ball then use your hands to weigh and distinguish whether it is heavier or lighter.

that wont work unless its significantly heavier or lighter.

has anyone got the answer yet?

Here's a long shot, Get some flour in a 4" tray & drop each ball 1 at a time from the same height & measure the crator & depth 11 should be the same & 1 diferrent. It may not be the correct answer but it should work. :D