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January 1, 2001 was a Monday and if you assign each day a number starting with Sunday as 0, you can use the number 1 for Monday in this equation. Each regular year pushes the day of the week of January 1 one day forward and each leap year pushes it two days forward. There are 25 leap years between 2001 and 2101 and 74 regular years. Therefore, the equation would be [1 + (25 * 2 + 74)] mod 7. The answer is 6, which is Saturday according to the assigned numerical value for days.

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