Solo Coder Solves 50-Year Mystery to Uncover Boggle’s Ultimate High-Scoring Board!

The word game Boggle has reached new heights, thanks to a relentless pursuit by Dan Vanderkam, a freelance software engineer. After 50 years of play, Vanderkam found the highest-scoring Boggle board, clocking in more than 1,000 words, with “replastering” being the longest.

Vanderkam, a former Google employee from New York, dedicated over 23,000 hours of computing power to this challenge. “At first, it seems impossible,” he said. He had only dabbled in Boggle during college but was captivated by the game’s intricate mathematical underpinnings.

Since 2004, he’s worked mostly alone, using Google’s computing resources to tackle this problem, while sharing updates on his blog here.

Boggle itself is simple: players use a 4×4 grid of lettered cubes. After shaking the cubes to randomize the letters, players race to find as many words as possible by linking letters horizontally, vertically, or diagonally. The longer the word, the higher the score.

Vanderkam’s groundbreaking board contains 1,045 words worth 3,625 points. In contrast, an average board scores about 140 points with roughly 100 words. Your chance of reproducing Vanderkam’s winning board at home is about one in 10 quintillion!

The search for the best Boggle board isn’t new. A 1982 article in Word Ways identified a high-scoring board but only achieved 2,195 points using computer assistance. Vanderkam believes that earlier methods missed out on optimal solutions due to a technique called "hill climbing." Much like a hiker navigating steep terrain, this approach may lead you to a peak but not the highest one.

Vanderkam’s techniques help him manage the sheer complexity involved. There are so many possible Boggle boards that examining each one directly is impractical—some calculations suggest it would take 800 million years to score them all, even with a speed of 200,000 boards per second!

To speed things up, Vanderkam categorized boards based on letter patterns. He also discovered upper limits for scores, allowing him to discard less promising options. The final piece of the puzzle came to him during a drive home, showcasing the power of what he calls “branch and bound” techniques.

While Vanderkam’s findings await peer review, he has made his code publicly available here. Despite the satisfaction of solving this challenging problem, he admits it’s bittersweet to see it come to an end.

This feat not only highlights the fun of Boggle but also reveals the depth of mathematical exploration in games. Vanderkam’s journey, one that combines passion and math, encourages others in the tech and gaming communities to explore challenges of their own.

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