imc

$2017$ There are $365$ days in a non-leap year. There are $7$ days in a week. Since $365=52\cdot 7+1$ (or $365\equiv 1(\mathrm{mod}7)$), the same date (after February) moves "forward" one day in the subsequent year, if that year is not a leap year. For example: $5/27/08$ Tue $5/27/09$ Wed However, a leap year has $366$ days, and $366=52\cdot 7+2$ . So the same date (after February) moves "forward" two days in the subsequent year, if that year is a leap year. For example: $5/27/11$ Fri $5/27/12$ Sun You can keep counting forward to find that the first time this date falls on a Saturday is in $2017$: $5/27/13$ Mon $5/27/14$ Tue $5/27/15$ Wed $5/27/16$ Fri $5/27/17$ Sat $\boxed{2017}$