BD-BDMO 2018 Problem 3

BdMO National 2018 Higher Secondary P3

Nazia rolls four fair six-sided dice. She doesn't see the results. Her friend Faria tells her that the product of the numbers is $144$ . Faria also says the sum of the dice, $S$ satisfies $14\leq S\leq 18$ . Nazia tells Faria that $S$ cannot be one of the numbers in the set { $14,15,16,17,18$ } if the product is $144$ . Which number in the range { $14,15,16,17,18$ } is an impossible value for $S$ ?