The anomaly being heavier in this example is important, since you have made it an assumption rather than a result of solving the puzzle.
The puzzle isn't about assuming the anomaly is lighter or heavier, and then working out which coin it is in 3 steps. It's about making no assumptions and finding out which coin is the anomaly and whether it is heavier or lighter.
It is easy to write out scenarios involving 3 weighings that depend upon knowing whether the coin is heavier or not, but the question asks for more.
Perhaps I'm misunderstanding your methods because you keep writing down weird notations. For instance:
and
I must seem like I'm nitpicking, but given the complexity of the problem, it is very confusing when working through a potential solution to come across variables that appear for a second and don't explain themselves.
As I stated before, if you could, please write step by step work in a similar form to the following:
(1) Separate 12 coins into 3 sets (X,Y,Z) of 4 coins each. GOTO (2)
(2) Weigh X against Y. If X = Y, GOTO (3). If X > Y, GOTO (4)
(3) Discard X and Y. Z contains the anomaly. Separate Z into 4 sets (Z1,Z2,Z3,Z4) of 1 coin each. GOTO (3a)
(3a) Weigh Z1 against Z2...
(4) ...
There are numerous answers to the question, but if you want me to put time into marking them I'd appreciate some format that can be read easily!
The puzzle isn't about assuming the anomaly is lighter or heavier, and then working out which coin it is in 3 steps. It's about making no assumptions and finding out which coin is the anomaly and whether it is heavier or lighter.
It is easy to write out scenarios involving 3 weighings that depend upon knowing whether the coin is heavier or not, but the question asks for more.
Perhaps I'm misunderstanding your methods because you keep writing down weird notations. For instance:
Quote:a) If za = zb, discard za and zc.Why do you discard zc? Surely you meant zb?
and
Quote:If zb = zd. z1 is heavier and the anomaly.Where on earth did z1 come from???
I must seem like I'm nitpicking, but given the complexity of the problem, it is very confusing when working through a potential solution to come across variables that appear for a second and don't explain themselves.
As I stated before, if you could, please write step by step work in a similar form to the following:
(1) Separate 12 coins into 3 sets (X,Y,Z) of 4 coins each. GOTO (2)
(2) Weigh X against Y. If X = Y, GOTO (3). If X > Y, GOTO (4)
(3) Discard X and Y. Z contains the anomaly. Separate Z into 4 sets (Z1,Z2,Z3,Z4) of 1 coin each. GOTO (3a)
(3a) Weigh Z1 against Z2...
(4) ...
There are numerous answers to the question, but if you want me to put time into marking them I'd appreciate some format that can be read easily!
