You have two sets of five coins. Each set has four real 30g coins and one 31g fake coin. It is easy to find the fake coins using a balance scale a total of four times, two weighings for each set.

Can you find a strategy which uses only three weighings?

(In reply to re: 3 simple steps by Charlie)

The line
1 3; 2 2      0  8 :   8   8   9 *
looks promising as it has only one 9.

Investigating we find:

1st Weigh Aabc against BCde

if Aabc = BCde
  the possibilities are
   Ad Ae Ba Bb Bc Ca Cb Cc
  2nd weigh A against C
  if A = C
   B is fake and weighing a against b will settle which of those is fake
  if A > C
   A is fake and weighing d against e will settle which of those is fake
  if A < C
   C is fake and weighing a against b will settle whether a, b or c is fake
  
if BCde > Aabc
  the possibilities are
   Bd Be Cd Ce Dd De Ed Ee
  2nd weigh CD against Be
  if CD = Be
   possibilities are Ce De Ed
   weigh C against D to determine which
  if CD > Be
   possibilities are Cd Dd
   weighing C against D settles it
  if CD < Be
   possibilities are Bd Be Ee
   weigh Bd against Ee to settle
  
if BCde < Aabc
  the possibilities are
   Aa Ab Ac Da Db Dc Ea Eb Ec
  2nd weigh A against D
  3rd weigh a against b

Edited on October 8, 2005, 2:53 am

Posted by Charlie on 2005-10-07 21:48:39