12 Ball Bearings Puzzle

nomore4s · 26 November 2009

beerwm said:
Seems that the first weighing has to be a 3v3.

4v4 = rogue ball in a group of [4 or 8]
3v3 = rogue ball in group of [6]

(ie.
if 3v3 balance, rogue ball is in other group of 6
if doesnot balance, rogue ball in current group
)

as we are looking for a scenario where it 'always works' so 3v3 > 4v4.

I'm not so sure about that, I think the groups have to be even otherwise you end up with too many possibilities to work it out in 3 weighings.

bellenuit · 26 November 2009

beerwm said:
Seems that the first weighing has to be a 3v3.

4v4 = rogue ball in a group of [4 or 8]
3v3 = rogue ball in group of [6]

(ie.
if 3v3 balance, rogue ball is in other group of 6
if doesnot balance, rogue ball in current group
)

as we are looking for a scenario where it 'always works' so 3v3 > 4v4.

The solution I posted works it out for all possible outcomes, using 4 X 4 first.

bellenuit · 26 November 2009

Robb said:
bellenuit, with that process you seem to end up at the third weighting with 3 possibilities...

Robb. I don't understand what you mean

Robb · 26 November 2009

Sorry, I didn't read your answer correctly (The formatting confused me a bit). Seems to make sense and covers all possible outcomes.
Using 4 groups of 3 results in the unsolveable case that I got to.

beerwm · 26 November 2009

bellenuit said:
The solution I posted works it out for all possible outcomes, using 4 X 4 first.

ahh my bad, i didnt realise i solution was posted

MACCA350 · 26 November 2009

bellenuit said:
Yes you are right, as I read it again. But some outcomes will require 4 weighings, but 3 is max allowed.

Yeah, I missed that part about 3 being the max allowed. Just having a go with your solution now.

cheers

MACCA350 · 26 November 2009

bellenuit said:
Carry on from where I left off.

Assume 1 to 4 is heavier than 5 to 8 after the first weighing

Second Weighing

Weight 1 2 and 5 against 4 6 and 9 (9 we know is a good ball bearing)

If 1 2 and 5 are heavier, then either 1 or 2 is the odd ball and is heavier, or 6 is the odd ball and is lighter.

Assume 1 2 and 5 are the heavier

Just running through this in the flash puzzle and got stuck here..........what's the next step if the scales are equal after this second weighing.

So far we don't know if the odd ball is heavier or lighter. It could be 3 if it's heavier or either 7 or 8 if it's lighter............can we solve this in one last weighing?

cheers

MACCA350 · 26 November 2009

Think I've worked it out.

Weigh 7 11 against 8 12.

If they are equal then 3 is the odd ball and is heavier
If 7 11 are heavier then 8 is the odd ball and is lighter
If 8 12 are heavier then 7 is the odd ball and is lighter

3 weighs again..............your solution is looking pretty solid

cheers

drsmith · 26 November 2009

Sorry nun. It looks like you'll have to hand that $59.95 over to bellenuit.

I too initially thought that 3+3 was a better option than 4+4 for the first weigh as this would eliminate a minimum of 6 ball bearings compared to a minimum of 4 for 4+4.

The problem with 3+3 is that if the odd ball bearing is in the 6 not weighed there is no further information from that weighing as to which one of those 6 is heavier or lighter.

4+4 only brings the minimum remainder down to 8 but of those 8 you also know that the odd bearing is either a heavier one in one group of 4 or a lighter one in a second group of 4. From there is it possible to isolate the odd ball bearing and it's weight relative to the others from a group of 3 at the final weighing. You need to get it down to 2 at the final weigh if starting with 3+3.

bellenuit · 26 November 2009

MACCA350 said:
Just running through this in the flash puzzle and got stuck here..........what's the next step if the scales are equal after this second weighing.

So far we don't know if the odd ball is heavier or lighter. It could be 3 if it's heavier or either 7 or 8 if it's lighter............can we solve this in one last weighing?

cheers

It was just a few lines further on....

Assume 1 2 and 5 are the same weight as 4 6 9

Then either 3 is heavier or 7 and 8 are lighter

Third Weighing

Weigh 7 against 8

If 7 is heavier than 8, then 8 is the odd ball and is lighter.
If 7 is lighter than 8, 7 is the odd ball and is lighter
If 7 and 8 are the same, 3 is the odd ball and is heavier

MACCA350 · 26 November 2009

bellenuit said:
It was just a few lines further on....

Assume 1 2 and 5 are the same weight as 4 6 9

Then either 3 is heavier or 7 and 8 are lighter

Third Weighing

Weigh 7 against 8

If 7 is heavier than 8, then 8 is the odd ball and is lighter.
If 7 is lighter than 8, 7 is the odd ball and is lighter
If 7 and 8 are the same, 3 is the odd ball and is heavier

<slaps own forehead> Doh! ..........that's what I get for skimming

cheers

12 Ball Bearings Puzzle

Commonsense isn't that common

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