Answer to Question #259765 in Discrete Mathematics for rtf

Question

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?

Answer 1

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.