# Professors house number puzzle

## Professors house number puzzle

A maths professor asked one of his students to visit his house regarding some work.
The student asked the professor his house number.
The professor replied in a strange way :

1. If my house number is a multiple of 3, then it is a number from 50 to 59.
2. If my house number is not a multiple of 4, then it is a number from 60 to 69.
3. If my house number is not a multiple of 6, then it is a numbre from 70 to 79.

Can you determine the professor's house number ?

Firstly, it can not be a number between 50 and 59.
The multiples of three between 50 and 59 are 51,54, and 57.
None of these numbers are multiples of 4, which means they would violate the second rule.
This means the answer is not divisible by 3.

The rules are being between 60 and 69 include being divisible by 6 but not by 3.
No number will ever satisfy this, so they're all out.

All that's left is to look at 70-70 for a number not divisible by 3 but is divisible by 4,
and the only number to satisfy this is 76.