Code Destine

8 Balls Weight Puzzle :- You have given a two-arm balance scale and 8 identical looking balls. One of the ball is heavier than rest of the 7 balls, which all are of equal weight. You have to find out the heavier ball by using two arm balance scale a minimum number of times.

Now try to solve this on your own...

Solution of 8 Balls Weight Puzzle :- 

8 balls weight puzzle can be easily solved in three weighing’s but this is not the solution interviewer is looking for, interviewer like you to solve this puzzle in only two weighing’s. Both solutions are as follows :-

Three weighing’s :-

First weigh :- Divide the eight balls into two set of 4 balls each and weigh (4 balls vs. 4 balls) it on the two-arm balance scale. Discard the 4 balls on the lighter side, leaving 4 balls.

Second weigh :- Take the remaining 4 balls, divide it into two set of 2 balls each and weigh (2 balls vs. 2 balls) it on the two-arm balance scale. Discard the 2 balls on the lighter side, leaving 2 balls.

Third weigh :- Take the remaining 2 balls, weigh (1 ball vs. 1 ball) it on the two-arm balance scale. The ball on the heavier side is the heavy ball.

Two weighing’s :-

First weigh :- Divide the eight balls into three sets, two sets containing 3 balls each and one set containing 2 balls. Weigh both 3 balls set (3 balls vs. 3 balls) on the two-arm balance scale. Now either the scale will balance or the scale will not balance and one side will be heavier.

Second weigh (a) :- If the scale is balanced, then the heavy ball must be in 2 balls set which was not weighed. Now take this 2 balls set and discard other two sets. Weigh (1 ball vs. 1 ball) both balls of the 2 balls set. The one that is on the heavier side is the heavy ball.

Second weigh (b) :- If the scale is not balanced, then the heavy ball must be on the heavier side of the scale, Now take 3 balls set on the heavier side of the scale and discard other two sets. Weigh any two balls (1 ball vs. 1 ball) from 3 balls set. If the scale balances, then the ball that didn’t get weighed is the heavy ball. If the scale does not balance, the ball on the heavier side is the heavy ball.

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