What day is it 100 days from Tuesday?

Question

Today is Tuesday. Solve in your head. What day of the week is it 100 days from now? Aim: under 10 seconds.

Accepted Answer

Only the remainder mod 7 matters. 98 = 14 	imes 7 is the nearest multiple of 7 below 100, so 100 = 14 	imes 7 + 2 \quad\Longrightarrow\quad 100 \equiv 2 \pmod 7. Tuesday + 2 days = Thursday. Takeaway. For "n days later" questions, reduce n mod 7 by jumping to the nearest multiple of 7 (multiples of 7 near round numbers are worth knowing: 98, 105, 350, 700). The same reduction handles "what day was it 40 days ago": 40 \equiv 5, so count 5 back, or, faster, 2 forward.

What day is it 100 days from Tuesday?

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