Software engineer Dan Vanderkam published a computational proof on the physics arXiv detailing the highest-possible scoring Boggle board configuration. Achieving a total score of 3,625 points, the grid contains more than 1,000 possible words and relies on a classic board game mechanism of 16 lettered cubic dice.
Cracking the Highest Possible Score in Classic Boggle
Software engineer Dan Vanderkam turned his attention to classic games, specifically Boggle, where players race against a time limit to find as many words as possible from a 4×4 grid of 16 lettered cubic dice. According to Ars Technica, Vanderkam detailed his quest in a preprint posted to the physics arXiv, presenting a computational proof for a board configuration that yields a maximum possible score of 3,625 points.
This configuration features more than 1,000 possible words. Among them, replastering
stands out as the longest word available on the board.
A Lonely Quest Rooted in Prior Attempts
While the problem might seem niche, Vanderkam acknowledged the singularity of his pursuit. He admitted to the Financial Times, As far as I can tell, I’m the only person who is actually interested in this problem.
Despite that solitary sentiment, he is not entirely alone in the history of the puzzle. An earlier attempt in 1982 successfully found an optimal board yielding 2,195 points. Vanderkam’s board configuration was previously suspected as a candidate for the highest possible score, but proving it using standard heuristic search methods proved exceptionally difficult.
Branch and Bound Techniques Over Brute Force
Tallying individual scores for every single board option would have made calculating a definitive proof nearly impossible through standard methods. To solve this, Vanderkam implemented an old-school computational strategy. According to Ars Technica, his solution involved grouping board configurations with similar patterns into classes and establishing upper bounds to discard clear losers, bypassing the need to score each individual board separately.
This branch-and-bound method allowed the computational proof to resolve the maximum possible layout. Vanderkam has documented his entire quest, the resolution, and the code he used extensively on his blog.
October Science Roundup Context
The Boggle computational proof was featured as part of an experimental monthly collection by Ars Technica highlighting science stories that nearly slipped through the cracks. Alongside the word game proof, October’s list of unique subjects covered by the outlet included the microstructural differences between regular and gluten-free spaghetti, capturing striking snakes in action, and exploring the mystery behind the formation of Martian gullies.
