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Among 12 identical looking golf balls there is one that is defective in weight. It is either heavier or lighter than the standard one. You have a balance. You can only weigh 3 times to find out which one is defective and whether it is heavier or lighter.
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Answer Posted / swati
In order to explain better, give each ball a number, said from 1 to 12. We also use ball zero to indicate a standard ball if that ball is identified as a standard ball.
Step 1. Take 8 balls to weight, ball 1, 2, 3, and 4 on the left, ball 5, 6, 7, and 8 on the right.
If they are balanced, go to Step 2-1.
If they are not balanced, go to Step 2-2.
Step 2-1.
At this time, you know the ball 1 to 8 are OK. Take ball 9, 10 and 11, plus a standard ball - ball zero. Just assume you have ball zero and 9 on the left and ball 10 and ball 11 on the right.
If they are balanced, go to Step 3-1.
If left side is heavier, go to step 3-2.
If right side is heavier, go to Step 3-3.
Step 2-2.
At this time, you know the ball 9 to ball 12 are standard balls. Assume the left side is heavier. Now you need to take 6 balls to weight the second time. You need to choose a standard ball - ball zero, ball 6 which might be lighter, and ball 3 which might be heavier, put them on the left side. Also you choose ball 2 which might be heavier, ball 5 and 7 which might be lighter. Notice that we change sides for ball 2 and ball 6.
If they are balanced, go to step 3-4.
If the left side is heavier, go to step 3-5.
If the right side is heavier, go to step 3-6.
Step 3-1.
From step 2-1, we know ball 9, 10 and 11 are standard balls. We just need to determine the ball 12 is heavier or lighter. We put a standard ball on the left, put ball 12 on the right.
If right side is heavier, the ball 12 is heavier.
If the right side is lighter, the ball 12 is lighter
Step 3-2.
From step 2-1, you know that either ball 9 is heavier, or one of statements should be true: the ball 10 is lighter or the ball 11 is lighter. We can put the ball 10 on the left, the ball 11 on the right.
If they are balanced, they should be OK, the ball 9 is heavier.
If the ball 10 is heavier, the ball 10 is Ok, ball 11 is lighter.
If the ball 10 is lighter, then the ball 11 is OK.
Step 3-3.
From Step 2-1, you know that either ball 9 is lighter, or one of statements should be true: the ball 10 is heavier or the ball 11 is heavier. We can put the ball 10 on the left, the ball 11 on the right.
If they are balanced, they should be OK, the ball 9 is lighter.
If the ball 10 is lighter, the ball 10 is Ok, ball 11 is Heavier.
If the ball 10 is heavier, then the ball 11 is OK.
Step 3-4.
From Step 2-2, you know ball 2, 3, 5, 6, 7 are standard balls. You can determine the ball 1 or ball 4 is heavier, or ball 8 is lighter. We can put ball 1 on the left and the ball 4 on the right.
If they are balanced, we are sure the ball 8 is lighter.
If the ball 1 is lighter, the ball 1 is Ok and ball 4 is heavier.
If the ball 4 is lighter, the ball 4 is OK, the ball 1 is heavier.
Step 3-5.
From Step 2-2, you know ball 2 and ball 6 are OK, because the change side does not affect the consequence. You can determine the ball 3 is heavier, or one of the statements is true: ball 5 is lighter or the ball 7 is lighter. We can put ball 5 on the left and the ball 7 on the right.
If they are balanced, we are sure the ball 3 is heavier.
If the ball 5 is heavier, the ball 5 is Ok and ball 7 is lighter.
If the ball 7 is heavier, the ball 7 is OK, the ball 5 is lighter.
Step 3-6.
From step 2-2, you know that the weighting result is changed because the ball 2 and ball 6 are exchanged. It really means that either ball 2 is heavier or ball 6 is lighter. You still have one more weight, I am sure you know how to do it!
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