Given a sequence of letters, we replace each letter with its position in the alphabet, and then we compute the product of all the numbers. For example, if the sequence was HAL, then we get the numbers 8, 1, 12 (because H, A, L are the eight, first, twelfth letters of the alphabet, respectively), and their product is 96. Find the smallest composite three-digit number that cannot be the result of computing this product for any sequence of letters.

Guest Apr 22, 2022

#2**0 **

Let's see:

100 = 2 x 2 x 25 or 4 x 5 x 5 so it works

101 is prime so it is excluded

102 = 2 x 3 x 17 so it works

103 is prime so it is excluded

104 = 2 x 2 x 26 or 2 x 4 x 13 so it works

105 = 3 x 5 x 7 so it works

106 = 2 x 53 ============ this can't be encoded; so the answer is 106

geno3141 Apr 22, 2022