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?

(In reply to New high by Joel)

120 looks good, though it took me a while to get the 3 tests to cover all possibilities.

If the piles are divided into (a,b,c) and (d,e,f,g,h) then:

First test:  ade  Answer: 2  then test d
                       Answer: 0  then test bf followed by bg
                       Answer: 1  then move to Second test: aefg

Second test: aefg  Answer:2 then test f
                       Answer: 0 then test b
                       Answer: 1 then test be

Edited on December 8, 2006, 10:18 am

Posted by Leming on 2006-10-19 15:50:48