Math Problems of the Month

 OSU-Marion

June  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.

 

  1. This one sounds easy...Was your first guess correct? How much does a fish weigh if it weighs 1 pound plus half its own weight?

 

 

  1. Show that in any group of 6 people (or more), there are always either 1) a group of three people who each know the other two or 2) a group of three people who are mutual strangers.

 

  1. Playing 5 card draw poker (with a normal deck of 52 cards), you draw Ace King Queen of Spades and the 5 of hearts and the 9 of diamonds. You discard the 5 and the 9 and draw two more cards.

    1. What is the probability that you draw to a royal flush?

    2. What is the probablility that you draw to a straight? (The cards don't have to be the same suit)

    3. What is the probability that you draw to two pair?

 

  1. Suppose your lights go out and you are trying to pick out matching socks from your sock drawer. You know that you have 12 black socks and 12 blue socks (any two socks of the same color will "match"). How many socks do you have to grab to guarantee that you have at least one matching pair? (You don't care which color)

 

 

  1. The object of this puzzle is to figure out which of the 12 patterns on the left can't be drawn with pencil in one continuous line so that you don't take the pencil point off the paper.

    You are not allowed to go over any part of the line twice, or cross it.