Question

A date is said to be lucky if, when written in the format M/D/YY, the product of the month and the day equals the two digits of the year. How many lucky dates will there be in 2018?

Answer 1

Answer: 5

Explanation:

We know that the two digits of the year are 18. So, we need to find the number of pairs (M, D) such that
`M\cdot D=18`.

Listing out the pairs, we get
`(M, D)=\{(1, 18), (2, 9), (3, 6), (6, 3), (9, 2), (18, 1)\}`.

However, the month cannot be more than 12, so we exclude the pair
`(18, 1)`.

Therefore, there are 5 pairs.