# 608 - Counterfeit Dollar

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Difficulty : easy

Solution Description :

Given maximum 12 coins, you can just test whether the three weighings are consistent with each coin being heavy or light.
Ans character character is must be in given characters.

Separate the given character to three part (even,up,down)
After separation
even part = union of all even part.
up part = intersection of all up part.
down part = intersection of all down part.
Now,
up part = remove all character which is match with even part.
down part = remove all character which is match with even part.

Example:
ED FG even //ED and FG in event part
CI AB down //CI in up part and AB in down part
A D up  // A in down part and D in up part

even part = ED ∪ FG = EDFG
up part = CI ∩ D = empty
down part = AB ∩ A = A

up part = empty - EDFG = empty
down part = A - EDFG = A
So ans is A

another example
ABCD EFGH even // ABCD and EFGH in even part
ABCI EFJK up // ABCI is down part and EFJK in up part
ABIJ EFGH even // ABIJ and EFGH in even part

even part = ABCD ∪ EFGH ∪ ABIJ ∪ EFGH = ABCDEFGHIJ
up part = EFJK
down part = ABCI

up part = EFJK - ABCDEFGHIJ = K
down part = ABCI - ABCDEFGHIJ = empty
So ans is K