Multiplicative Dates

If you read the previous post containing Math Problems for 2024, then you already know what a multiplicative date is. But in case you missed it, here’s the definition again:

A multiplicative date is one in which the product of the month and date is equal to the (two-digit) year. For instance, today — January 24, 2024 — is a multiplicative date, because 1 × 24 = 24.

The question I asked in that previous post was, how many multiplicative dates will there be in 2024?

But I’m revisiting this topic again today, because today is the first multiplicative date of a year that has more multiplicative dates than any other year this century. That’s right, no year 20XX has more multiplicative dates than 2024.

Of course, there’s no reason to stop there. There are quite a few interesting questions related to multiplicative dates:

1. How many years this century have no multiplicative dates?
2. Which two consecutive years have the most multiplicative dates combined?