What day was it 45 days ago?

Question

Today is Sunday. Solve in your head. What day of the week was it 45 days ago? Aim: under 10 seconds.

Accepted Answer

Reduce 45 mod 7. The nearest multiple of 7 below 45 is 42 = 7 	imes 6, so 45 = 42 + 3 \quad\Longrightarrow\quad 45 \equiv 3 \pmod 7. Going back 3 days from Sunday: Saturday, Friday, Thursday. Equivalently, going back 3 is the same as going forward 7 - 3 = 4: Monday, Tuesday, Wednesday, Thursday. Same answer, so pick whichever direction is the shorter count. Takeaway. "Days ago" is just a backward reduction mod 7. If counting backward feels awkward, flip it: back r equals forward 7 - r. Here back 3 equals forward 4, both land on Thursday.

What day was it 45 days ago?

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