NYT Pips Puzzle Solutions and Walkthrough for Thursday, July 30

Each day, the New York Times offers a quiet arena for the mind in the form of Pips, a grid-based domino puzzle that asks players to impose order on a field of colored constraints. On July 30th, three puzzles of ascending difficulty invited solvers to practice the ancient art of systematic reasoning — beginning with what is known, tolerating uncertainty, and following logic until the last piece falls into place. Forbes has stepped in as a patient guide for those who find themselves at an impasse, offering not just answers but the reasoning behind them.