Each of the 9 letters of the word POSTERIAL has been assigned a different integer value between 1 and 9. With those same values, the product of the letters in each of the following words is as indicated:
P L O T = 144
S A I L O R = 6,048
A L E R T = 840
S A T I R E = 10,080
A P O S T L E = 5,760
a) Determine the value of each of the letters of POSTERIAL.
b) Altogether there are about 369 words (without repeated letters) that can be drawn from POSTERIAL ( A prolific nine-letter word). What is the least number of these that would have allowed to unequivocally deduce the values of the letters of POSTERIAL.