The May, 2008 Problem of the Month


A True MATHEMATICS Problem!!


Using the grid below, there are many ways to spell the word MATHEMATICS by starting at the top of the grid and moving down through the letters. At each level, you must move to a letter which is below and to the immediate left or right of the letter you are at.

How many unique ways can we spell out the word mathematics by moving from the top letter and ending at the bottom letter? 
                   M
                 A   A 
               T   T   T
             H   H   H   H
           E   E   E   E   E
         M   M   M   M   M   M
           A   A   A   A   A
             T   T   T   T
               I   I   I
                 C   C
                   S


  Here is one possible way to spell out
  mathematics:


                   M
                  / 
                 A   A
                  \ 
               T   T   T
                    \
             H   H   H   H
                    /   
           E   E   E   E   E
                  /                               
         M   M   M   M   M   M
                   \      
           A   A   A   A   A
                    \  
             T   T   T   T
                      \
               I   I   I
                      /
                 C   C
                    /
                   S


Submit solutions in PSA 216 to Problem of the Month care of Richard Reynolds, or via email at rich@math.asu.edu


See http://math.asu.edu/~rich/puzzles/main.html for a web page view of this problem and past problems with solutions.