Each letter of the alphabet is assigned a value $(A=1, B=2, C=3, ..., Z=26)$. The product of a four-letter list is the product of the values of its four letters. The product of the list $ADGI$ is $(1)(4)(7)(9) = 252$. What is the only other four-letter list with a product equal to the product of the list $PQRS$? Write the letters of the four-digit list in alphabetical order.
Let's first find the product of the list PQRS. We know that the product of a four-letter list is the product of the values of its four letters. The value of P is 16, the value of Q is 17, the value of R is 18, and the value of S is 19. These values are 24 and 12, and the letters that correspond to these values are X and L, respectively. So the letters with these values are X and L. So the other four-letter list is $LQSX$.

