there are 6 balls all of same weight except one ball. u r
given a weighing balance. in how many trys can u find the ball
tat has different weight? (the ball can b heavier or lighter
than the rest)
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Answer Posted / lion251
Three tries will always be enough.
Start by weighing balls 1,2 together (left) against balls 3,4 (right).
If the balance is equal, then we know that balls 1,2,3,4 are normal. Then weigh ball 5 against a 'normal' ball (one of 1,2,3,4). If the balance is equal, then 6 is the different ball, else 5 is different.
If the balance tipped was unequal on the first measurement, then we know that either one of the two balls on the lower side is too heavy, or one of the two balls on the higher side is too light.
Then, weigh the two balls that were on the lower side against each other. If one side goes down, then that is the different ball, and it is too heavy. If the scales balance, then weigh the balls that were on the higher side in the first measurement against each other. The side that goes up holds a ball that is too light.
Thus, three measurements will always be enough.
It is interesting to know that, in the same three measurements, you can even find out a different ball from a group of 12(!). That is quite a bit more difficult, but even then, three measurements will be enough in all cases (provided you choose your weighings extremely carefully)
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