The 2nd of June is a Thursday in a certain year. Which day of the week is the 3rd of July in that year?

Question

If it was a Friday on 1 January 2016, what was the day of the week on 31 December 2016?

Answer 1

Calendar day-of-week questions come down to counting the number of days between the two dates and reducing that count modulo $7$.

Option (A), Thursday: this would only hold if the gap were a whole number of weeks, but $31$ days is not a multiple of $7$.
Option (B), Friday: this matches a gap of $1$ day beyond a whole number of weeks, but the actual remainder is $3$, not $1$.
Option (C), Saturday: this matches a remainder of $2$ days, again short of the true remainder.
Option (D), Sunday: June has $30$ days, so June 2 to July 3 spans $31$ days. $31 \bmod 7 = 3$, and counting $3$ days forward from Thursday gives Friday, Saturday, Sunday.

The correct remainder of $3$ days past Thursday places July 3 on a Sunday, option (D).

Answer 2

Calendar day-of-week questions come down to counting the number of days between the two dates and reducing that count modulo $7$.

Option (A), Thursday: this would only hold if the gap were a whole number of weeks, but $31$ days is not a multiple of $7$.
Option (B), Friday: this matches a gap of $1$ day beyond a whole number of weeks, but the actual remainder is $3$, not $1$.
Option (C), Saturday: this matches a remainder of $2$ days, again short of the true remainder.
Option (D), Sunday: June has $30$ days, so June 2 to July 3 spans $31$ days. $31 \bmod 7 = 3$, and counting $3$ days forward from Thursday gives Friday, Saturday, Sunday.

The correct remainder of $3$ days past Thursday places July 3 on a Sunday, option (D).

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