To find the first day of the year 1666, we need the day of the week on January 1, 1666.
Number of completed years = 1665 years
Breakdown of 1665 years = 1600 years + 65 years
Odd days in 1600 years = 0 (as 1600 is a multiple of 400)
In the remaining 65 years, number of leap years = 65 ÷ 4 = 16 (quotient)
Number of ordinary years = 65 − 16 = 49
Odd days in 65 years = (16 × 2) + (49 × 1) = 32 + 49 = 81 odd days
Converting 81 days into weeks: 81 ÷ 7 = 11 weeks and 4 odd days.
Total odd days until December 31, 1665 = 0 (from 1600 years) + 4 (from 65 years) = 4 odd days.
Number of odd days for January 1, 1666 = 4 (completed years) + 1 (current day) = 5 odd days.
According to the mapping, 5 odd days corresponds to Friday.
Hence, the first day of the year 1666 was Friday.

Key Points
Number of odd days in 100 years = 5
Number of odd days in 200 years = 3
Number of odd days in 300 years = 1
Number of odd days in 400 years = 0
An ordinary year has 1 odd day, and a leap year has 2 odd days.
Day code mapping: 0 = Sunday, 1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, 5 = Friday, 6 = Saturday.

Alternate Method
Using the formula: Day = (Date + Month Code + Century Code + Year + Leap Year Code) ÷ 7
For January 1, 1666:
Date = 1
Month Code (January) = 0
Century Code (1600s) = 6
Year = 66
Leap Year Code (66 ÷ 4) = 16
Total = 1 + 0 + 6 + 66 + 16 = 89
Remainder of 89 ÷ 7 = 5
Day code 5 corresponds to Friday.
Hence, the correct answer is Friday.