I came across with this question (from http://www.paypal.com/cgi-bin/webscr?cmd=p/gen/jobs-engineers-outside ).

"You are given twelve balls. All are the same size and weight, except one which is heavier or lighter than the others. Using a balance scale, can you determine the odd ball in three weighings?"

Note: to start, you have to assume that the odd ball is heavier than the others, or lighter (not indeterminate between the two). If you don't know whether the odd ball is either heavier or ligher, you may not solve the problem above, at least not in three weighings...

Try to solve the above problem (easy), but for me the problem becomes more interesting if you do not know in advance whether the odd ball is either lighther or heavier than the rest, what is the minimum weighings do you have to do in order to know which one is the odd ball? Anybody wants to give your number for this minimum weighing (in this case)?

cheers,
:beer:

I love racking my brain on these. OK, let's see...

1. weigh 4 balls on each side. If they are equal, the odd one is in the next batch of 4

2. take 3 of these 4 and weigh them against 3 of the others that are known to be equal weight. If they are equal, then the one that has not been weighed is of the unequal weight. If the new sample is heavier, then take 2 of the three and weigh them against each other. If these are equal, then the one that was not weighed is the odd one. If one is heavier, then it is the odd one.

That's how it should be done in at most 3 steps, assuming that the odd one is heavier.

very cool... I think all solutions would be similar... Mine goes initially with 5 balls against another 5 balls... then 2 balls agains 2 balls... and at this point, our solutions are indetical.

I am still more interested with the revised problem... I will try to get my number (the minimum number of weighings before you can find out which one is the ood ball, assuming you do not know whether the odd ball is ligher or heavier)... still crunching my brain :D ...

cheers,
:beer:

1. Firstly weigh 4 vs 4.
2.(a)If these are equal in weight then the odd one is in the other 4.
Take 3 of these and weigh them against 3 of the others already verified as equal weight.
i. If these are heavier, then take 2 of them and weigh them against each other. If these are equal then the one not weighed is the odd one and heavier. If one is heavier then it is the odd one and heavier.
ii. If these are lighter, then take 2 of them and weigh them against each other. If these are equal then the one not weighed is the odd one and lighter. If one is lighter then it is the odd one and lighter.
iii. If these are equal the one left over is the odd one, with one more weigh against a proven normal weight to determine whether it is lighter or heavier.

(b) If these show themselves as having the odd one by being lighter or heavier then take 3 of the relatively heavier + 2 of the relatively lighter group and weigh them against the 4 left + the other that was of the relatively heavy group.
i. If these are equal then weigh the 2 light ones against each other to determine which light one is the odd one.
ii. If the 3 heavier group + 2 lighter group weighs heavier then the odd one must be amongst the 3 of the relatively heavier group. Then weigh 1 against a second. If one is heavier then it is the odd one. If they are equal then the 3rd was the odd one and heavier.
iii. If the 3 heavier group + 2 lighter group weighs lighter then the 2 of the realtively lighter group would be weighed against each other. If one is lighter then it is the odd one. If they are equal then the ball that was
relatively heavy and weighed with the 4 normals was the odd one and heavier.

welll i would just pick up all of them... then i would know which is heavier or lighter right? :) who needs a scale?

Isn't the left one always lighter? :D

Weight a group of 4 against another group of 4. If one group is heavier, use that group. If not, use the other group that have not been weighed.

Now split the heavier group into 2 goups or 2 and wiegh them. Then take the heavier group of two and split it into 2 groups of 1. One will be heavier.

Originally posted by Racin' Rob
Isn't the left one always lighter? :D

Weight a group of 4 against another group of 4. If one group is heavier, use that group. If not, use the other group that have not been weighed.

Now split the heavier group into 2 goups or 2 and wiegh them. Then take the heavier group of two and split it into 2 groups of 1. One will be heavier.

Hmm, I thought I already answered that one.

Originally posted by Racin' Rob
Isn't the left one always lighter? :DThe left one is always "bigger" and therefore I would think "heavier." ;)