A lucky year is one in which at least one date, when written in the form day/month/year, has the following property. The product of the month times the day equals the last two digits of the year. For example, 1944 is a lucky year because it has the date 11/4/44 where $$11 \times 4 = 44$$. From 1951 to 2000 how many years are not lucky? Give proper explanation for your answer.

A year with last two digits N (from 51 to 99, plus 00) is lucky if N can be written as a product of a valid month (1 to 12) and a valid day for that month (up to 31). Checking each year's last two digits against all possible month-day factorizations identifies the years with no valid factorization. These are 2000, 1953, 1958, 1959, 1961, 1962, 1967, 1971, 1973, 1974, 1979, 1982, 1983, 1986, 1989, 1994 and 1997, a total of 17 years.