The first thought is to consider the transition from Christmas to New Year's Day of the following year. But the trick is that the question asks about one given year. Since New Year's Day of the following year is the same day of the week, within one year, Christmas is either one or two days of the week after that of that same year's New Year's Day, depending on whether the year in question is a leap year, as there's an intervening February. That is the number of days of the week that New Year's Day advances, and Christmas matches that following New Year's Day.

To answer the question that immediately comes to mind when one doesn't think about it enough, Christmas of 1750 in England and its colonies, including New Jersey, where I live, Christmas (Old Style, Julian) was a Tuesday (Jan 5, 1751, Gregorian New Style). New Year's Day of 1751 was March 25 (Old Style, Julian), a Monday (April 5, 1751, (New Style, Gregorian)).  The shift to New Style (NY Day on Jan. 1) and Gregorian did not take place until 1752.

But then, of course, Christmas of 1751 was a Wednesday (Jan. 5, 1752, Gregorian).  New Year's Day was celebrated for the first time as January 1, but still Julian, so the 1-week separation started then. It was only later in the year (September) that the calendar itself was changed from Julian to Gregorian. It was only the beginning of 1752 in which Britain still used the Julian calendar, but in the New Style of starting the year on January 1.