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Grapeland To Applecity

Hint:
Step one: First you want to make 3 trips of 1,000 grapes 333 kilometers. You will be left with 2,001 grapes and 667 kilometers to go.
Step two: Next you want to take 2 trips of 1,000 grapes 500 kilometers. You will be left with 1,000 grapes and 167 kilometers to go (you have to leave a grape behind).
Step three: Finally, you travel the last 167 kilometers with one load of 1,000 grapes and are left with 833 grapes in appleland.
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Eight Balls

Hint:
Put three balls on each side of the scale. If the arms are equal, you know the heavy ball is one of the two remaining. If the arms are unequal, take the three balls on the heavier side, pick two and weigh them against each other.
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