You are given 8 equal sized bars of silver labeled a to h. You know for a fact one of them is fake, and the only measurable difference is weight. However you do not know if the fake bar is heavier or lighter. You are also given a balance scale which can be used to compare weight between two bars or sets of bars. However, you are restricted to using the scale only twice. Find the fake one in 2 weighing. Given: Bars e,f,g,h are collectively lighter than bars a,b,c,d.
we know either a,b,c or d is heavier, or e,f,g or h is lighter
on one side, a, b, and e, on the other, c, d and f
if the first weighing is equal
this means either g or h is the lighter. we just have to put them on each side to see wich one is the lighter
if the left part is heavier
this means either a or b is heavier, or f is lighter. we just have to weight a and b, if a is heavier, the fake bar is a. if b is heavier, it's the fake bar. if the weigh is equal, f is the fake one.
if the right part is heavier
this means either c or d is heavier, or e is lighter. we just have to weight c and d, if c is heavier, the fake bar is c. if d is heavier, it's the fake bar. if the weigh is equal, e is the fake one.