jmc

Question

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.

Accepted Answer

The product of the list PQRS is (16)(17)(18)(19)=(2^4)(17)(23^2)(19). Every value must be at most 26, so we cannot change the primes 17 and 19. However, (2^4)(23^2)=(2^23)(2^33)=(12)(24), which represents LX. Thus, the four-letter list with a product equal to that of PQRS is LQSX.