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This question already has an answer here:

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.

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marked as duplicate by Glorfindel, JonMark Perry, rhsquared, Oray, generalcrispy May 11 '18 at 12:55

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  • $\begingroup$ Is the balance scale can be used to compare weight between two bars or two sets of bars? $\endgroup$ – athin May 11 '18 at 11:11
  • $\begingroup$ You can compare between two or sets of bars. $\endgroup$ – PythonMonkey May 11 '18 at 11:24
  • $\begingroup$ Sorry for the mistake it's bars. $\endgroup$ – PythonMonkey May 11 '18 at 11:26
  • $\begingroup$ That just explains the algorithm for number of steps required for N number of balls. What I ask is not the number of steps. $\endgroup$ – PythonMonkey May 11 '18 at 11:43
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first weighing

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

second weighing

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.

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  • $\begingroup$ d can't be lighter than f, as a,b,c,d are collectively heavier than e,f,g,h and since 7 of them weigh exactly the same, d can't be the lighter fake one. $\endgroup$ – PythonMonkey May 11 '18 at 12:14
  • $\begingroup$ Yeah the way you worded the question I don't think is very appropriate...Even given which group of bars is lighter it would be impossible to determine which of the bars is the lightest without actually having the bars to weigh. This answer IS the solution. $\endgroup$ – Colton May 11 '18 at 13:01

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