In a certain year, January had exactly $4$ Mondays and $4$ Fridays. What was the day on $2^{\text{nd}}$ October the previous year?

Question

In a certain year, the month of January had exactly $4$ Mondays and $4$ Fridays. What was the day on Gandhi Jayanti $(2^{\text{nd}}$ October $)$ the previous year?

I am not sure how to approach this one, any ideas?

Answer 1

As January has 31 days, there are three days that there were 5 of (pigeonhole principle). The calendar says they must be contiguous, so they must have been Tuesday, Wednesday, and Thursday. So Jan 1 was Tuesday. Then just count back.