This problem is a combination of a traditional weights and scales puzzle and a probability puzzle.
You are given the traditional scale balance and a set of 10 coins. You know that in this set of coins there are four fakes - two that are heavier than the others, and two that are lighter. Furthermore, you know that a light coin plus a heavy coin will perfectly balance two genuine coins. You are permitted only two weighings with the balance and asked to pick one of the 4 fake coins. What strategy should you use to maximize your success rate, and what would your success rate be?
What if you were given one genuine coin to start with (though still leaving you with 10 unknown coins)?
(In reply to
re(2): ~50% by Cory Taylor)
Thanks -- but the weighing 1 vs 1 was Ryan's idea originally. I was trying more complex things, and I don't know if I would have thought of this without reading his post.
However, my calculator tells me that 4/10 + 6/10*4/9 + 6/10*5/9*4/8 = 83.3%
The fractions make sense to me (4 chances in 10 the first coin is bad, 6/10*4/9 the first is good and the second is bad, 6/10*5/9*4/8 that both the first and second are good and then the one you randomly pick from the remaining 8 is bad).
Am I missing something here?
re(3): ~50%
