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?
(In reply to Solution
1.First number the wrench 1 to 5.
2.weigh( 1st) (1,5) and (2,3).If a.equal,weigh(2nd) 5,4.If still equal ,none is different.
b.(1,5) heavy, so either 1 is heavy or one of (2,3)is light.
So in the 2nd weighing weigh, (4,2) and (3,5)-If same,then 1st wrench is heavier.Else the lighter of the (2,3) is defective on the lighter side.
c.(1,5) Light,so by similar logic,so either 1 is light or one of (2,3)is heavy.
So in the 2nd weighing weigh, (4,2) and (3,5)-If same,then 1st wrench is lighter.Else the heavier of the (2,3) is defective on the heavier side.