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 Two sets of Coins (Posted on 2005-10-07)
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?

 See The Solution Submitted by Brian Smith Rating: 3.5000 (2 votes)

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 solution | Comment 3 of 7 |
(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

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