ANSWER TO PUZZLE 1

27 potatoes!
The last man left eight after taking a third of what he saw. So eight was two thirds of what he saw. So he saw 12. So the second man left 12.
The second man left 12 after taking a third of what he saw. So 12 was two thirds of what he saw. So he saw 18. So the first man left 18.
The first man left 18 after taking a third of what he saw. So 18 was two thirds of what he saw. So he saw 27.

Or 8 is two thirds of 12, 12 is two thirds of 18, 18 is two thirds of 27.

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