What day is it 1000 days from Wednesday?

Question

Today is Wednesday. Solve in your head. What day of the week is it 1000 days from now? Aim: under 10 seconds.

Accepted Answer

Only the remainder of 1000 mod 7 matters. Jump to the nearest multiple of 7 below 1000: since 7 	imes 142 = 994, 1000 = 994 + 6 \quad\Longrightarrow\quad 1000 \equiv 6 \pmod 7. So count 6 days forward from Wednesday: Thursday, Friday, Saturday, Sunday, Monday, Tuesday. A faster mental route: 6 \equiv -1 \pmod 7, so instead of counting 6 forward, count one day back from Wednesday, which is Tuesday. Same answer, less counting. Takeaway. For huge day counts, find a nearby multiple of 7 (700, 994, 1001, \dots) and keep only the remainder. When that remainder is 5 or 6, going backward (-2 or -1) …

What day is it 1000 days from Wednesday?

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