A forum for good logic/math puzzles.

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Postby Jayraj » Fri Nov 30, 2018 1:33 pm UTC

In a room, there are 115 closed barrel of wines of different taste, numbered 1 to 115.

Just outside the room, there are 115 people eagerly waiting to taste those wines.

They are handed each a ticket with their turn and lined up in ascending order at the entrance.

They are briefed with a simple rule:

"Ticket number one gets to take a cup of wine from every barrel.

Number two from every second barrel, number three from every third, number four from every fourth and so on.

If you find that your barrel is open then you close it after use, else you open it and keep it open."

The first person gets in, opens each barrel and takes one cup of wine from each of them and exits.

After the 115th person has gone through the room, can you deduce which barrel of wine is still open and only seven person tasted that particular wine?

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Joined: Fri Feb 05, 2016 5:42 pm UTC

Re: Wines

Postby Tirear » Fri Nov 30, 2018 6:27 pm UTC

If we have some number with prime factorization an*bo*cp*...
Then the number of positive integer factors is (n+1)*(o+1)(p+1)*...
Since 7 is prime, the only solution is a single prime number taken to the 6th power. 26=64, and using any other prime gets a number greater than 115, so the answer is barrel 64 (used by tasters 1,2,4,8,16,32,64).

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