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I do my laundry every 20 days. Last week, laundry day fell on a Friday. On what day of the week will laundry fall next?
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Let us associate the numbers 0, 1, 2, 3, 4, 5, 6 to represent the weekdays from Sunday to Saturday respectively.
Last week, laundry day fell on a Friday. So, the number for Friday is 5. Since, I do my laundry every 20 days, so needs to subtract 20 from 5 and take the modulo 7, since a week contain 7 days.
-15 (mod 7) ≡ –1 (mod 7) ≡ 5–1 (mod 7) ≡ 4 (mod 7)
Thus, 1 − 15 ≡ 4 (mod 7)
The day for the number 4 is Thursday. Therefore, on Thursday day of the next week will laundry fall.