a puzzle i need help with?
#1
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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 ***** (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 ***** 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
Anyway it goes like this:
you have 12 identical looking metal ***** (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 ***** 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
#2
GOT IT!!
You take the 12 ***** 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 *****
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??
You take the 12 ***** 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 *****
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??
#3
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You are now left with 3 *****
Split into 3! put 1 on each side of the scales and keep 1 to one side!
Split into 3! put 1 on each side of the scales and keep 1 to one side!
if the scales balance you have the heaviest ball in your hand.
if the scales don't balance then...
#5
Originally Posted by mj
put any two of the three ***** on the scales.
if the scales balance you have the heaviest ball in your hand.
if the scales don't balance then...
if the scales balance you have the heaviest ball in your hand.
if the scales don't balance then...
But you need to know whether its heavier or lightier so my theory is completly wrong!!
Need to start again
#6
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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.
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.
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#10
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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
Si
#12
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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 ***** & 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
Si
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Owned (nearly)
...forget ye old fashioned balancing scales.....
pick 6 random ***** 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 ***** weigh the same.
say the ***** 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............
..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 ***** is 600g, the difference +/- of this figure will be the weight of the oddball multiplied by 2, thusly the oddball is (600-537)x2=126g for the oddball.[/mj's theory of weighabilty]
pick 3 random ***** 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...x2:
..You have 3 ***** (ET) ).
...over to you puzzle solvers, I'm too pissed.
...forget ye old fashioned balancing scales.....
pick 6 random ***** 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 ***** weigh the same.
say the ***** 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............
..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 ***** is 600g, the difference +/- of this figure will be the weight of the oddball multiplied by 2, thusly the oddball is (600-537)x2=126g for the oddball.[/mj's theory of weighabilty]
pick 3 random ***** 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...x2:
..You have 3 ***** (ET) ).
...over to you puzzle solvers, I'm too pissed.
#16
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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 ???
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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.
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Andy Tang
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06 December 2001 01:42 AM