You have 11 visually identical coins. One of them is marked genuine (and you know which one this is). Out of the remaining 10 coins, all but one of them are also genuine, but you don't know which ones. The remaining odd coin has a different weight, either heavier or lighter than the others.

You have a regular two-pan balance. This works like you expect: you load a certain number of coins to each side, and the balance will tell you the heavier pan (or whether they have equal weight).

How many weighings are necessary in the worst case to find the odd coin and determine whether it weighs more or less than genuine coins?

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