What day is 250 days from Friday?

Question

Today is Friday. Solve in your head. What day of the week is it 250 days from now? Aim: under 10 seconds.

Accepted Answer

Reduce 250 mod 7. A handy nearby multiple is 245 = 7 	imes 35 (recall 35 is a multiple of 7, so 350, 245, and 210 all are too): 250 = 245 + 5 \quad\Longrightarrow\quad 250 \equiv 5 \pmod 7. Count 5 forward from Friday: Saturday, Sunday, Monday, Tuesday, Wednesday. Or use 5 \equiv -2 \pmod 7 and step two back from Friday: Thursday, Wednesday. Same result, fewer steps. Takeaway. Memorize the multiples of 7 that hide near round numbers (245, 350, 700) so you can snap any day count down to a remainder of 0 through 6. For remainders of 5 or 6, counting backward is the shortcut.

What day is 250 days from Friday?

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