there are 8 balls. one ball is slightly heavier than the others. you have to find out exactly which ball is the heavier one with minimum number of trials. you are given a mechanical scale like the one below to weight items.
you are not given any weighing units to measure. you are given just the balls and the scale. how will you determine the heavier ball and in how many trials. ?
hint: you can weigh the balls against each other.
click here for answer
the normal answer is to take four balls on left scale, and four balls on right scale. if one weighs down, take those 4 again weigh 2 on left and 2 on right. take the heavier scale's two balls, and again weigh them against each other to get the heaviest ball. but there is another method to figure out the heaviest ball in just 2 attempts. Think again and Scroll down to find the answer
unlike first method, take three balls on left scale, and three on right leaving two on the table. take the three balls whole scale is heavier and keep one of them seperately on the table and weigh again one ball on each scale.now if one of the scale goes down, then that ball is the one we are looking for. if both scales are equal, then the third ball we placed on the table is the answer. now you might ask, what happened to the first two balls that we forgot to weigh ? that comes into picture if during first attempt of three balls on each scales, if both scales are equal. then it means none of the 6 balls are heavier leaving us with the two balls to weigh against each other. in either case only two attempts are needed to figure out the heaviest ball.
2 trials.
ReplyDeleteTrial 1: Weigh the balls 3 against 3. Now, they either balance out, or one side falls being heavier.
If they balance out
Trial 2: Weigh the remaining 2 balls against each other. The heavier side is the odd ball.
If one side falls in Trial 1,
Trial 2: Weigh 2 of the balls from the heavier side against each other. One falls, that is the odd ball. They balance, the third unused ball is the odd ball.