I have a batch of 16 coins, each coin weights either 9g, 10g, or 11g. I split the pile into halves and compare each half on a balance scale and the result is unequal.
Then I take each pile of 8 and perform the same process: split each pile in half and compare the halves from that pile. Both times I get unequal results.
I then repeat the process with the four piles of 4. Again all four weighings are unequal.
I keep going to make eight more weighings comparing the individual coins in each pair formed previously. Again all weighings are unequal.
What are the possible compositions of the original pile of 16 coins?