please solve this riddle

[sham1983]

We have total 12 balls in which 11 balls have same weight but only ball has different weight. You have allow three times to weight all balls and remove one ball which has different weight and tell me the weight of that ball.

 

[Domski]

Maybe:

Split the balls into 3 sets of 4 balls. Weigh 2 sets of 4 and find out if equal or not. From that you will know if one of the sets of balls weighed is lighter or if they are the same, if the same then the lighter set must be the set that you haven't weighed.

Split the lighter set of balls into sets of 2 balls. Weigh again to find the lighter set of 2 and then weigh each of the balls from the ligher set to determine which is the lightest ball.

Dom

 

[SydneyGeek]

Similar:

Weigh 6 on each side, take the lighter set and split to two sets of 3.
Now weigh any two of the lighter triplet. If they balance, the lighter one is the one you didn't weigh in the third go. If they don't you will know which is the lightest.

Denis

 

[Andrew Fergus]

This took me a wee while to work out but if you don't know if the different ball is heavier or lighter then this should do it:

Weigh 1 to 4 vs 5 to 8.

If 1 to 4 = 5 to 8, then weigh 1 & 9 vs 10 & 11. If these are the same weigh 1 vs 12, otherwise 1 & 12 vs 9 & 11. Different outcomes give varying answers as to which ball is different and whether it is lighter or heavier.

If 1 to 4 < 5 to 8, then weigh 1, 2 & 5 vs 3, 4 & 7. If these are the same weigh 10 vs 8, but if 1+2+5 < 3+4+7 then weigh 1 vs 2, else 3 vs 4. Again, different outcomes for the 3rd weigh give different answers as to which ball is different and whether it is lighter or heavier.

See if you can work out the 3rd sequence if 1 to 4 > 5 to 8.

Andrew

P.S. Done properly, you should be able to cover all 24 instances of balls 1 to 12 being either heavier or lighter.

 

[Stormseed]

Hello,

As the OP says, that you are allowed to weigh the balls for 3 times and get the weight of the 12th ball which infact is a lighter ball. We now have an *idea* as how to go about finding out the lighter ball.

How do we arrive at a conclusion in respect to the weight of the ball ? Anyone having some pointers ?

 

[schielrn]

How do we arrive at a conclusion in respect to the weight of the ball ? Anyone having some pointers ?

I would assume if we are weighing the balls, we are using some sort of scale to get weight. When I first saw this, I thought of Domski's approach.

 

[cornflakegirl]

But all the approaches rely on old-fashioned scales - measuring one (set of) ball(s) against another - so no actual weights involved.

 

[MrKowz]

If it is a scale that gives an actual weight instead of a scale that compares weight....

1) Weigh a random ball
2) Weigh a second random ball
    If (1) and (2) weigh the same, then you know that is the weight of the heavier ball.
    If (1) or (2) is lighter than the other, then the lighter one is the weight of the lighter ball.
3) Weigh ALL balls, the total weight = 11*(weight of heavier ball) + weight of lighter ball.

 

[Stormseed]

How about this ?

 

[markelly]

OK, but the question is about the weight of the lighter ball as well.
I don't think you can do it with three steps only.