This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: It might not yet be the phenomenon that is Wordle, but for hundreds of thousands of players, Digit Party has scratched the itch of a casual brain teaser to break up their day. Players arrange numbers on a 5-by-5 grid, earning points whenever identical numbers touch on adjacent or diagonally connected squares.
They can then compare their score to the puzzle's maximum score that the game spits out at the end of a round. There's just one problem: The game was lying. Or rather, its creators were.
For more than three years, Vincent Vatter, Ph.D., at the University of Florida and Robert Brignall, Ph.D., at The Open University in the United Kingdom didn't know how to calculate the true high scores. "We knew there was this issue, but we didn't know how to fix it," said Vatter. "We had a number we knew nobody could beat.
Most of the time it was actually reachable, but about 5% of the time it wasn't, and we had no way to tell the difference. We knew it this whole time, and it bugged us." Now, Vatter and Brignall report that they've discovered how to compute the true high score of every possible combination of numbers. Out of the last three years' 1,096 daily puzzles, the game "lied" 55 times.
The average error was just 2 points or so; the maximum was 6 points. With a game's typical maximum score of around 150 to 200 points, the wrong scores were off by a percentage point or two. The team published their findings Aug. 25 in Math Horizons.
Although the stakes are small for this casual puzzle, the underlying mistake is common in optimization. The best solution for each individual part of a problem doesn't always combine into the best overall solution, a challenge that also appears in scheduling, logistics and manufacturing. In Digit Party, the player scores based on how well they arrange the same number next to itself.
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