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Fair dice & Impossible 18+

Source: Bangladesh National Mathematical Olympiad 2018

February 27, 2019
number theorycountingBdmoDice

Problem Statement

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 144144. Faria also says the sum of the dice, SS satisfies 14≤S≤1814\leq S\leq 18 . Nazia tells Faria that SS cannot be one of the numbers in the set {14,15,16,17,1814,15,16,17,18} if the product is 144144. Which number in the range {14,15,16,17,1814,15,16,17,18} is an impossible value for SS ?
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