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The following word problems require both math and logic to solve, so put on your thinking cap!
Three pirates on an island
Three pirates arrive on an island after relieving a merchant of his bars of gold. They pile their uncounted booty in the center of the island and fall asleep while guarding it. After a while, the first pirate wakes up and decides to take his share of the gold and hide it. So he buries his fair share of the gold bars under a palm tree and goes back to sleep. The second pirate wakes up and takes what he thinks is his fair share and buries it beside a boulder; then he goes back to sleep, too. Then the third pirate wakes up, takes his fair share, and hides it under a boat and goes back to sleep. In the morning, the pirates wake up and discover that eight bars of gold are still in the pile. How many bars were in the pile in the beginning?
Answer: If each pirate took one third of the booty, working backward, the 8 bars that remain must be two-thirds of what was there when the third pirate took his share. So the third pirate saw 12 bars, took his 4, and left 8. If the second pirate left 12 bars, then 12 was two-thirds of what he saw, so he saw 18 bars — he took 6 and left 12. The first pirate left 18 bars, which was two-thirds of what was there in the beginning. One-third of 27 is 9, leaving 18 bars. There were 27 bars of gold when the pirates all went to sleep.
Pouring four quarts
A farmer needs to add exactly 4 quarts of weed killer to the fertilizer that he's preparing to spread over his field. Unfortunately, he has only a 3-quart container and a 5-quart container. He can't just guess; the accuracy of his measurement is most important. How can he measure exactly 4 quarts with the two containers he has? (There are several possible solutions, but the farmer wants the one that takes the fewest number of steps.)
Answer: The farmer fills the 5-quart container and empties 3 quarts from that container into the 3-quart container, leaving 2 quarts in the 5-quart container. Then he empties the 3-quart container and pours the 2 quarts from the 5-quart container into the 3-quart container, leaving room in the 3-quart container for another quart. He fills the 5-quart container again and pours 1 quart into the 3-quart container that already contains 2 quarts. That leaves exactly 4 quarts in the 5-quart container.
Where did the dollar go?
Randy, Andy, and Sandy go out for lunch together. The waitress brings them a bill for $30, so each pays $10. When the waitress takes the cash to the register, she realizes that she overcharged them; she should have charged only $25. So, when she brings the change back, Randy, Andy, and Sandy each take $1 and leave the other $2 as a (horrible) tip. Because each friend paid $10 and got $1 back, each person actually paid $9. Multiply $9 by 3 and add the $2 tip, and you get $27 + $2, or $29. What happened to the other dollar?
Answer: This puzzle definitely belongs in the category of sleight of hand. Randy, Andy, and Sandy actually paid only $9 each, totaling $27. The bill was $25, so subtract $25 from $27 and you have the $2 tip.
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