You have 12 coins , one of them is fake , the fake coin is identical in apperance but slightly differnt in weight . You have a balanced scale , the scale only tells you which side weighs more than the other.
theese are modern coins ,the fake coin is not nessacairaly lighter.
You have to use only the 12 coins , no extra scales no pencil marks on the scale.
what is the smaller number to times to use the scal to find the fake coin.
3 times most of the time, 4 times worst case scenario:
divide 12coins into 4 bags of 3 coins(A,B,C,D)
do A vs B
if balanced do (2->) A vs C: if balanced then fake is in D if not then fake in C
if not balanced do (2->) A vs C: if balanced then the fake is in B if not then fake in A
so we used 2 times the scale to isolate 3 coins (x,y,z) and if fake is not in D then we know if fake is lighter or heavier (D worst case scenario)
do x vs y
if balanced then fake is z
if not balanced then
if fake was in A,B,C we know if it is heavier or lighter so we know if it is x or y
if fake was in D then
x vs z : if balanced then fake is y if not balanced then fake is x
edit: i saw the answer, and using 3 times the scale is enough, so my method isn't the best one
Edited 4/16/2015 18:41:16