To determine the day of the week for a given date, we need to use the concept of "modulo 7 arithmetic." We assign a number to each day of the week, starting with Sunday as 0, Monday as 1, and so on up to Saturday as 6. Then we use the following formula:

day of the week = (day number + month code + century code + year code) % 7

Where:
- day number is the day of the month (e.g. 20 for July 20th)
- month code is a number based on the month (see table below)
- century code is a number based on the first two digits of the year (see table below)
- year code is a number based on the last two digits of the year (see table below)



To calculate the month code, we use the following table:

Month | Code
------|-----
January | 0
February | 3
March | 3
April | 6
May | 1
June | 4
July | 6
August | 2
September | 5
October | 0
November | 3
December | 5

For March, the month code is 3.



To calculate the century code, we use the following table:

Century | Code
--------|-----
1700s | 4
1800s | 2
1900s | 0
2000s | 6

Since 1991 falls in the 1900s, the century code is 0.



To calculate the year code, we use the following formula:

year code = (year + (year / 4)) % 7

For 1991, the year code is:

year code = (91 + (91 / 4)) % 7
= (91 + 22) % 7
= 4



Now we can plug in the values and calculate the day of the week for March 6th, 1991:

day of the week = (6 + 3 + 0 + 4) % 7
= 13 % 7
= 6

So March 6th, 1991 falls on a Wednesday.