Optimizing Solving NYT's Pips Game

*this is an ongoing writeup - I'll probably finish up the solver in a week or so

A few days ago, one of my co-TAs introduced me to the New York Times' Pips game. For those who haven't played, the main goal is to tile dominos across a grid with certain constraints:

Here's a small snippet of today's Easy board:

Pips board and domino collection