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Pitchers and Poison (A Sour Defeat in the UK version) is a puzzle in Professor Layton and the Diabolical Box.

Puzzle

US Version

Two men, known here as 1 and 2, are playing a strange game. First, both men put their empty pitchers on the table. Next, a judge brings a pitcher filled with purple poison and places it in either spot A or spot B. The judge then starts shifting the poison from one pitcher to any adjacent pitcher over and over. After moving the liquid 55 times, the owner of the poison filled pitcher must drink its contents.

If you were the judge and secretly wanted 1 to win, would you place the poison-filled pitcher down in spot A or spot B?

UK Version

Two men, known here as 1 and 2, are playing a strange game. First, both men put their empty pitchers on the table. Next, a judge brings a pitcher filled with vinegar and places it in either spot A or spot B. The judge then starts shifting the vinegar from one pitcher to any adjacent pitcher over and over. After moving the liquid 55 times, the owner of the vinegar-filled pitcher must down it in one! Ugh!

If you were the judge and secretly wanted 2 to drink the vinegar, would you place the pitcher down in spot A or B?

Hints

Click a Tab to reveal the Hint.

US Version

Grab a few water glasses and try the puzzle out for yourself--minus the poison, of course.

The principle that determines where the poison is should soon become obvious.

UK Version

Grab a few water glasses and try the puzzle out for yourself, minus the vinegar, of course.

The rule that determines where the vinegar ends up should soon become obvious.

US Version

If you stopped after five pours instead of 55, what would be different?

UK Version

If you stopped after five pours instead of 55, would anything be different?

US Version

Isn't it funny how on every odd-numbered pour, the poison ends up in the middle of the three pitchers?

UK Version

Isn't it funny how on every odd-numbered pour, the vinegar ends up in the middle of the three pitchers?

Solution

Incorrect

US Version

Normally, you might need some encouragement here to try again, but as there are only two possible answers to this puzzle, you probably know the solution now.

UK Version

Normally, you might need some encouragement to try again, but as there are only two possible answers to this problem, you now know the solution...

Do try to work out the reasoning behind the solution before answering, though!

Correct

Nicely done!

US Version

The liquid changes pitchers 55 times, which is an odd number of pours. Regardless of where you set down your pitcher, whichever pitcher sits in the middle of the three will always contain the poison after an odd number of pours.

Therefore, in order for 1 to win, the poison-filled pitcher must go in spot B, because doing so will put 2's pitcher in the middle, thus guaranteeing the poison ends up in his pitcher.

UK Version

The vinegar changes pitchers 55 times, which is an odd number of pours. Regardless of where you place your pitcher, whichever pitcher sits in the middle of the three will always contain the vinegar after an odd number of pours.

Therefore, in order for man 2 to drink, the vinegar-filled pitcher must go in spot B, because doing so will put man 2's pitcher in the middle, thus guaranteeing the vinegar ends up in his pitcher.

A big thanks to http://professorlayton2walkthrough.blogspot.com

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