Question: A man wants to have a party in thirty-one days where he will be serving his 1000 barrels of wine. The only problem is that one of his enemies poisoned one of the barrels. The poison kills any man who drinks any of the wine in about 30 days, give or take a few hours. The man has 10 plants that are also killed by the poison in 30 days and can be used to test the wine. How can identify the single poisoned barrel of wine?
Answer: To do this the man must create 1000 unique groups from the 10 plants in which each group has between 1 and 10 plants, and give each plant wine from a different barrel. He can then throw away the barrel of wine that corresponds to the group that died from the wine.
Question: Joe deals himself and his friend John some cards from a deck of cards (not the same amount). If John gives Joe some cards Joe will have 4 times as many cards as John. If Joe gives John the same number of cards he will have 3 times as many cards as John.
How many cards does each man have and how many cards do they trade?
Answer: Joe has 31 cards, John has 9, and they trade 1 card.
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