The Return to Monkey Island mop puzzle might be one of the first in the game, but true to form, it can be a little elaborate if you're playing on hard mode. While Return to Monkey Island does provide a hint book that you can get from the International House of Mojo, it's not always specific about puzzle steps, and you might not want to check it constantly...
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How to get the mop in Return to Monkey Island
Source: PC Gamer (opens in a new tab)