Math Problems of the Month

OSU-Marion

October 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.

• Two pedestrians have one bike to share between them. They travel as follows: the first one rides the bike for some time, then drops it and continues walking in the same direction, while the second follows him by foot. Eventually, the second one finds the bike and rides it until he catches up to the first one. Then he gives the bike to the first one etc. Assuming that they both walk at 4 mph and both ride the bike 10 mph, what is the speed of their travel?
  

• Can you figure out this riddle? What's your first guess? Are you sure???
• A man has a nice portrait in his library. When he was asked whom it represented, he replied:
  
     Uncles and brothers
        Have I none,
     But that man's father
        Is my father's son.
  
  What relation was the subject of the portrait to that man?
  
  

• Someone took a cut out of a letter and made a single fold in it. The result was the following figure. What was the original letter? Note: It was not an "L"...

• Here is a problem in Graph theory that should be good for anyone in Math 116 (or anyone else for that matter...)
• Start at the "top" dot on this maze and follow the paths through every dot without following any pathway more than once.
  
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• Try to do the same for the following map... (Is it even possible?)