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?

I used a similar style to Jer's method of splitting the coin sets in half, and continously splitting the coins with each sucessive test to ultimately get a test of 2 coins. The very last test would involve splitting the last 2 coins, and getting a '0' or '1' to figure out which one is radioactive. Getting 2 coins on one of the halves would result in minimal amount of tests, so it isn't a sure-fire answer if 1 coin makes you use more tests. The key is that there has to be a mutual method that works in the scenario that 1 or 2 coins end up in one split. The largest amount of coins to rule out a radiocactive coin would be 2. So if you go backwards and times it by 2^X. X representing each test. X=1 would result in 2 coins. X= 5 32 coins split 16 run 1 test test at 8, then at 2 and 1. 5 total tests. The other split would be 5 also, not going over 10 total tests.

Posted by Cyriis on 2006-10-20 13:13:34