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Number of Tuesdays in five consecutive calendar years taken together is exactly $260$. Which day of the week was $1st$ January of the first of these five years?

On the basis of given information the day will be either Wednesday or Thursday. How? I did not understand the solution of this question

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A year has either $365$ or $366$ days, which is $\lfloor 365/7\rfloor = 52$ complete weeks ($364$ days) plus $1$ or $2$ extra days.

Over 5 years, then, we have $5\times 52=260$ complete weeks and $5,6,$ or $7$ extra days, depending on whether the period includes $0,1,$ or $2$ leap years.

Since we are given that the period only includes $260$ Tuesdays we cannot have $7$ extra days (a full week), so $5$ or $6$ extra days would mean that the first year would need to start on a Wednesday or Thursday to avoid including a Tuesday in those extra days.

Note that zero leap years in a $5$-year stretch is unusual to the point that no-one alive today has lived throughout such a period.

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