In a certain year there were exactly four Fridays and four Mondays in January. On what day of the week did the 20th of January fall that year ?
Step-by-step Solution:
- The month of January always has 31 days.
- 31 days is equal to 4 full weeks plus 3 extra days (since 31 = 4 × 7 + 3).
- This means that in any given January, three days of the week will occur five times, and the other four days of the week will occur only four times.
- The three days that occur five times will always be consecutive (e.g., Saturday, Sunday, Monday).
- The problem states there were exactly four Mondays and four Fridays.
- This tells us that Monday and Friday are part of the group of days that occurred only four times.
- For this to be true, the three consecutive days that occurred five times must be the days between them: Tuesday, Wednesday, and Thursday.
- The three days that occur five times in a 31-day month are always the first three days of that month.
- Therefore, January 1st must have been a Tuesday.
- We now need to find the day of the week for the 20th, knowing the 1st was a Tuesday. A quick way to do this is to add weeks:
Final Answer: The 20th of January fell on a Sunday.