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?

It's also possible to find a solution if a balance scale is used...

Call the 4 new spanners a,b,c,d and the standard spanner s.

Firstly, put s & a on one side of the scale and b & c on the other.

If s+a = b+c, then try s vs d.

• if s=d, then there are no defective spanners
• if s>d, then there is a lighter spanner (d)
• if s<d, then there is a heavier spanner (d)

If s+a > b+c, then try b vs c

• if b=c, then there is a heavier spanner (a)
• if b>c, then there is a lighter spanner (c)
• if b<c, then there is a lighter spanner (b)

Similarly, if s+a < b+c, then again try b vs c

• if b=c, then there is a lighter spanner (a)
• if b>c, then there is a heavier spanner (b)
• if b<c, then there is a heavier spanner (c)

 

Posted by fwaff on 2004-07-02 10:26:09