Day 15:002: A puzzle a day

I received this on my birthday - I'd actually ordered it myself before Christmas as a general puzzle to have around, but it arrived while Exile #2 was squirreling things away that arrived for me, so it understandably became a birthday present (from myself).

Supposedly there is "at least one solution" for each date. At first glance we thought that meant 365 (or 366) puzzles, but since it includes the days of the week, it's a lot more than that.

Exile #4 solved it on Saturday, I solved it on Sunday and Exile #3 has solved it the last two days. I wonder how long we'll keep the streak going.