Math Problems of the Month

OSU-Marion

September 2005

Try your hand at these problems. Each month I will post a few of my favorite math problems and puzzles. Some can be solved by algebra, some need some clever intuition, some need a little elbow grease. I hope you enjoy them as much as I do.

Submit answers to Dr. Maharry in MR 370 or at maharry@math.ohio-state.edu.

I will post the names of those who submit correct solutions outside my door and on my web site.

• Write equations that equal the numbers 0 to 10 using exactly four 4's.
• You can use operations + (add), - ( subtract), * (multiply), / (divide), or ( ) (parenthese). No other numbers are allowed. For example, ( 4 + 4 ) - ( 4 + 4 ) = 0 or 4/4 - 4/4 = 0 or 44 - 44 = 0

• You need exactly four gallons of water, yet you only have two buckets: one five gallons and the other seven. How do you measure out four? Can you measure every number of gallons from one to twelve? How?

• Raymond Smullyan has made a career of writing logic problems. His most famous have to do with a mythical island of Knights and Knaves. Knights always tell the truth, and Knaves always lie.
  
  As you approach the island, you spot three inhabitants on the shore. You call out to them, "Are you Knights or Knaves?" The first says something but you do not hear what he says, so you ask, "What did you say?" The second inhabitant says, "He says he is a Knight, he is and so am I." The third responds, "He is a Knave, but I am a Knight." What are the three inhabitants really?

• Here is a problem about rearranging some figures. But do the areas change?
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