You have N coins, 2 of which are radioactive. You have a radioactivity detector which can test any subset of the coins at a time, and return the number of radioactive coins in the group (i.e. it returns 0, 1 or 2). You have to find the radioactive coins, using not more than 10 tests. What is the largest N for which this is possible?

Top number you can be garaunteed to find them in 10 tries or less is 48

48 divided into 3 stacks 16 16 16 = 2 tests will tell you where the 2 coins are, worst case they will be in two different piles.

Each stack divided in half each time will take an additional 4 tests to determine the coin. (each division only requires one test, as the second half of the pair will always be the opposite) 16->8->4->2->1.

4 x2 (two stacks) +2 to get to 16=10 tests.

Explanation may be a bit wonky, but I'm positive 48 is the upper (lower?) limit to garauntee identification.

Posted by Tyryt on 2007-08-14 17:38:02