There are 4 wrenches just unpacked from a box. They all look the same. There might be one defective item which is either heavier or lighter. Fortunately there is a fifth one that is standard. If you can use a scale to weigh only 2 times, can you find out:

1. Is there a defective wrench?

2. If there is a defective item, is it heavier or lighter?

Wrenches denoted as: 1, 2, 3, 4 & S(for Standard)
Scale: L - Left , R - Right
On a balancing scale:
1st weighing: L - 1&2 , R - 3&S

If they balance then 4 is defective,
2nd weighing: L - 4 , R - S
Will determine if 4 is heavier or lighter.

If they do not balance,
2nd weighing - L - 1 , R - 2
This will reveal which wrench (1,2,or 3) is defective and if it is heavier or lighter.

For instance, if the result of the first weighing was 1 & 2 were heavier, the second weighing will have one of two findings. If 1 & 2 balance then it would indicate that 3 was light (given that we already know S is standard). If they do not balance then the heavier of the two would be the defective. Thus determining in two weighings which is defective and its'weight relative to the others. If 1 & 2 were light the same process would be used.

Posted by Patricia Stamets on 2004-07-04 22:59:23