There are at least two algorithms. The one you outline here feels more like the one I use (and, coincidentally, Art Benjamin[0][1][2] uses), whereas Conway used one of his own devising called the Doomsday Algorithm[3].
So you're right, it's not that hard, but be aware that you may not be thinking of the algorithm Conway used.
So you're right, it's not that hard, but be aware that you may not be thinking of the algorithm Conway used.
[0] https://en.wikipedia.org/wiki/Arthur_T._Benjamin
[1] https://math.hmc.edu/benjamin/
[2] https://www.ted.com/talks/arthur_benjamin_a_performance_of_m...
[3] https://en.wikipedia.org/wiki/Doomsday_rule