You are given a task of locating one faulty coin out of 99 identical in appearance coins i.e. 98 of equal weight and one of a lesser weight; and to achieve it within seven weighings, using a balance scale.

Sounds familiar and easy (3⁷>99)?

Familiar? Yes.

Easy? Not quite!

How can you accomplish it if no coin may be weighed more than twice ?

Bonus task: After devising the requested procedure please generalize:
How many coins (n-1 normal and one lighter) can be resolved within k weighings?

Even after considering Ady's correction in the comments, this seems impossible to me.  I'd be very interested in hearing the solution.

 

Posted by tomarken on 2014-06-30 16:50:58