**Problem 3**

At different time during the day, Ms. Segura will drop a letter to be typed into her secretary’s tray. Ms. Segura numbers these letters consecutively from 1 to 6 as she writes them. When there is time, her secretary takes the top letter out of the tray and types it. Which sequence below could not be the order in which the secretary typed the letters? Explain your answer.

a) 5,4,6,3,2,1 b) 3,5,4,2,6,1 c) 4,2,5,6,3,1 d) 2,4,6,5,3,1

[Problem
submitted by Roger Wolf, LACC Chairman of Mathematics,]

**Solution for Problem 3:**

The answer is c)
because if the first letter the secretary takes to type is the fourth letter
(which implies that the letters are piled 4,3,2,1),
the next one to type is

the third letter if the fifth and/or sixth have not been placed
in the tray while the fourth letter is being typed

or the fifth or sixth letter if one or both have been placed
in the tray while the fourth letter is being typed.