Attempting to clarify the question:

Christmas Day is 25th December. The immediately-following New Year's Day (1st January of the following year) is always exactly a week later. Thus, in a given holiday season (24th Dec to 2nd Jan, for example), they fall on the same day of the week.

You are asserting that, at least twice in the period 1970 to 1980, this didn't happen.

Have I understood the question correctly?
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-- roger