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:
 Is there a defective wrench?
 If there is a defective item, is it heavier or lighter?
This seems simple, which probably means I'm approaching it incorrectly.
First, we assume we don't know the weight of the standard wrench, and just that it's a standard. The first weighing then is to determine the exact weight of the standard.
Second, we weigh together all four of the wrenches in question. If the weight is exactly four times that of the standard, there is no defect. If it is greater than four times the standard, there is a heavier wrench. Similarly, if it is less than four times the standard, there is a lighter wrench.

Posted by Eric
on 20040702 09:17:57 