Weekly  Mathematics  Problem  #99

Anyone can take a piece of paper and apply four 90-degree rotations
so that it returns to its starting position. Show how one can take a
piece of paper and apply FIVE 90-degree rotations so that it ends up
in the same position it started in.


     This is Macalester College
     Problem of the Week #801.




All midshipmen submitting correct solutions to problem #99 by
3:30 pm on Tuesday, October 12, win a cookie. The best
solution will be posted on the problem bulletin board.

A solution is "correct" if it gives a correct sequence of rotations and explains why it works; a
solution is "best" if it includes the clearest correct explanation.  Submit solutions to Prof. Hanna
at mathprob@usna.edu, or via the mailbox in Chauvenet 301.



Midn. Martyn and Milev are entitled to cookies for correctly computing the odds that a three pieces of a
line segment can be formed into a triangle as 25%. A solution is posted on the Chauvenet lab-deck
bulletin board.