Did your calc professor not assign enough homework to fulfill your incredible math appetite? Have no fear! We have a wonderful selection of math problems to keep you busy until the wee hours of the morning... you wouldn't want your brain to rust over, would you? I didn't think so!

• 1. Three men walk into a hotel and order a delicious dinner, and their bill comes to $30. So each man pays $10 towards the cost and goes up to his room to do whatever. But later that night, the hotel manager looks at the bill and realizes, oops, he overcharged them by $5! So he calls over a bellboy, explains the situation, gives him 5 one-dollar bills, and tells him to go give the men the money back. The bellboy, not wanting to deal with the change, instead gives each man 1 dollar, and pockets the other 2 himself. Ultimately, each man paid $9 toward the room and the bellboy kept 2 for himself. 9 x 3 = 27, plus the 2 the bellboy kept is 29... what happened to the 30th dollar?
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• 2. Joe's happiness is proportional to the function (w^2)c (w squared times c), where w stands for daily consumption of glasses of wine, and c stands of daily consumption of number of cigars. Wine costs $3 a glass and cigars cost $2 each. His daily budget for both is $100. How should he divide his money between wine and cigars to maximize his happiness? Assume he does not have to buy integer numbers of either cigars or wine.
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• 3. A bartender has a three pint glass and a five pint glass. A customer walks in and orders four pints of beer. Without a measuring cup but with an unlimited supply of beer how does he get one pint in either glass?
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• 4. A box contains two coins. One coin is heads on both sides and the other is heads on one side and tails on the other. One coin is selected from the box at random and the face of one side is observed. If the face is heads, what is the probability that the other side is heads?
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• 5. John and Dan have the following conversation...

  John: I forgot how old your three kids are.
  Dan: The product of their ages is 36.
  John: I still don't know their ages.
  Dan: The sum of their ages is the same as your house number.
  John: I still don't know their ages.
  Dan: The oldest one has red hair.
  John: Now I know their ages!

  Assuming John's some sort of genius, how old are the little urchins?
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• 6. Assuming both players take turns, what is the probability the player who goes first will lose at Russian roulette using a gun with six chambers?
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• 7.
  

  It's impossible to draw this figure without taking the pen off the paper, redrawing any lines, or other trickery. Why?
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• 8. You have nine pearls, eight are real and one is fake. All the real ones weigh the same and the fake weighs less than the real ones. Using a balance scale twice how can you weed out the fake one?
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• 9. If it takes Dr. Vazanna 20 hours to paint a house and it takes Dr. Knight 30 hours, how long will it take if they work together yet independently?
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• 10. (No real math required on this one.) One one side of a river are three humans, one big monkey, two small monkeys, and one boat. Each of the humans and the big monkey are strong enough to row the boat. The boat can fit one or two bodies (regardless of size). If at any time at either side of the river the monkeys outnumber the humans the monkeys will eat the humans. How do you get everyone on the other side of the river alive?
  (Solution)