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[jrbraves26]

You have 50 coins that all look exactly the same. One of them is fake and weighs a few grams more than the others. Given a balance scale (not a triple beam scale), what is the fewest number of weightings you could use to find the fake coin? Explain.

[Pankaj Varma]

Spoiler for Spolier added

You need 3 or 4 weighings
Divide into 3 heaps - 17, 17, and 16 and weigh the first two. You now know which heap has the fake coin.
Repeat process with the selected heap - 6,6,5 or 5,5, 6 as the case may be, and weigh the first two.
Repeat again 2,2,2 or 2,2,1. If the single coin is fake, no further weighing is required. Else
You have to do a 4th weighing if the fake coin is in a group of 2.

Edited by bonanova, 15 March 2013 - 05:58 AM.
Add spoiler

[bonanova]

You have 50 coins that all look exactly the same. One of them is fake and weighs a few grams more than the others. Given a balance scale (not a triple beam scale), what is the fewest number of weightings you could use to find the fake coin? Explain.

 

Spoiler for Looks like

You have 50 possibilities Each weighing distinguishes among 3 cases. 3x3x3 = 27, so you'd need a fourth weighing for this case.