Jun Xiang uses 4 letters K, L, M and N to form a pattern. The first 25 letters are shown below. What letter is in the 338th position? $\text{K L M M K L N K L M M K L N K L M M K L N K L M M} \dots$
$\text{1st}\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\text{25th}$

1. Identify the repeating pattern and its length

The pattern is $\text{K L M M K L N}$.
The length of one complete cycle is $7$ letters.

2. Find the number of complete cycles and the remainder for the 338th position

$338 \div 7 = 48 \text{ R } 2$
This means there are $48$ complete cycles, and the $338$th letter is the $2$nd letter of the next cycle.

3. Determine the letter at the remainder position

The $2$nd letter in the pattern $\text{K L M M K L N}$ is $\text{L}$.