You have to sort five weights weighing 51g, 52g, 53g, 54g, and 55g. You have a balance scale with which you can compare the weights. But after solving so many sorting puzzles, it is starting to break down.

If the difference between two weights is greater than 1.5g, the scale will correctly determine which side is heavier. If the difference between the weights is less than 1.5g or equal, the scale will indicate the weights are equal.

Sort the weights in the smallest number of weighings.

(In reply to 5 weighings by i_wish)

"I)                   Find out the relation ship between:

A ___ B (>, < or =)

A ___ C

A ___ D

 

The only possible instances you can get are:

a)      >,>,> (A>B,A>C,A>D)

b)      >,>,= (A>B,A>C,A=D)

c)      >,=,=  etc

d)      >,=,<

e)      =,=,<

f)        <,<,<"

 

Why not for example >,<,< or >,<,=?

"II)                

A) suppose you got case a) >,>,>  

then it follows that A is 55 since it is larger than the three others. It can’t be 54 since the balance will display 54=53. This also leaves us to conclude that E is 54!"

There are not just 3 others; there are 4 others, so A is not necessarily 55.

Posted by Charlie on 2004-09-08 15:44:02