Pickled Onion Puzzle

Level pending

Three weary travellers came to an inn, late in the evening, and asked the landlord to prepare some food. "All I got is pickled onions," he muttered. The travellers replied that pickled onions would be fine, thank you very much, since the alternative was no food at all. The landlord disappeared and eventually came back with a jar of pickled onions. By then, all the travellers had fallen asleep, so he put the jar on the table and went off to bed, leaving his guests to sort themselves out. The first traveler awoke. Not wishing to make a pig of himself, and not knowing what anyone else had already eaten, he took the lid off the jar, threw away an onion that looked bad, are one third of the onions that remained, put the lid back on the jar, and went back to sleep. The second traveller awoke. Not wishing to make a pig of himself, and not knowing what anyone else had already eaten, he took the lid off the jar, threw away two onions that looked bad, are one third of the onions that remained, put the lid back on the jar, and went back to sleep. The third traveller awoke. Not wishing to make a pig of himself, and not knowing what anyone else had already eaten, he took the lid off the jar, threw away three onions that looked bad, are one third of the onions that remained, put the lid back on the jar, and went back to sleep. At this point the landlord returned and removed the jar, which now contained six pickled onions. How many were there to start with?

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