To get a year's digit product, multiply the year's digits. For example, between 1900 and 2000, the 2 years 1913 and 1931 each have a digit-product of 27. What is the largest integer n for which n of the years from 1900-2000 have the same non-zero product?

Question

To get a year's digit product, multiply the year's digits. For example, between 1900 and 2000, the 2 years 1913 and 1931 each have a digit-product of 27. What is the largest integer n for which n of the years from 1900-2000 have the same non-zero product?
A. 2
B. 3
C. 4
D. 6

So are asking to multiply the digits of 1900 and 2000??

Reiny · Accepted Answer

so the year can't have any zeros
smallest possibe = 1911
largest is 1999

since they all have to start with 99, variations of products can only come from the last 2 digits
1914 1941 1922 all produce the same product
1942 1924 1918 1981 all produce the same product
same thing for 1916 1961 1923 1932

so unless I am not interpreting this the right way,
my answer would be n = 4