There are 10 ball of some (can be not the same) weights, we need to find the heaviest one, but no more than one weighing can be wrong.
I think that we need 19 weighings. We will weigh two balls twice and, if the results are not equal, we will do third weighing and leave the heaviest ball.
Can it be done in less number of weighings or why it can not be less than 19?
I think that we need 9 weighings if all weighings are true and we need to find out which one of them was false, but I thought about transitivity between the results and now I don't think that it is enough to prove that there can not be less weighings.