Expert: Richard J. Raridon - 11/16/2008

Question
I am 14. This was a problem given to me at class and I am a little confused.  
         P
        L L
       U U U
      S S S S

I need to find how many combinations to spell the word PLUS
going top to bottom and only touching once (diagonally)right or left.  
 I understand that
P = 1
L = 2
U = 3
S = 4
and using fundamental counting, the answer would be 24.
  But since it is giving a specific requirement and not
all combinations - I don't think this is correct.
 I think I am on the right track, but need a little advice.


Answer
You can't look at it that way because of only going diagonally.
Number them as follows: L1 L2 U1 U2 U3 S1 S2 S3 S4
Now the possibilities are
P L1 U1 S1
P L1 U1 S2
P L1 U2 S2
P L1 U2 S3
P L2 U2 S2
P L2 U2 S3
P L2 U3 S3
P L2 U3 S4
That's all