Two Math Professors Admit Their Puzzle Game Digit Party Overstated High Scores for Years

Hundreds of thousands of players have tried a free online game called Digit Party, stared at a string of numbers, and felt that little jolt of pride when the app told them how close they’d come to the perfect score. Turns out that number was often wrong. The two math professors who built the game have now admitted that for three straight years, the “perfect score” they showed players was sometimes just plain incorrect, and in one case it was off by six whole points.

Writing in the mathematics magazine Math Horizons, the creators of Digit Party have admitted the mistake. Their game asks players to place digits from 1 to 9 onto a 5-by-5 grid, one at a time, scoring points whenever two matching digits land next to each other. After each round, the app compares a player’s score to what it claims is the best possible score for that exact puzzle. That comparison, it turns out, was built on a shortcut that looked right almost all the time but wasn’t actually correct.

Behind the mistake is a reason that makes it more than an ordinary bug. Finding the true best possible score for a 25-digit puzzle is a surprisingly hard math problem, one that took the creators years, some serious computing power, and a nudge to a professional mathematician to finally solve.

How Digit Party’s Scoring Shortcut Went Wrong

Every day, Digit Party deals out 25 digits one at a time. Players see the current digit and a preview of the next one, but must place each digit on the grid before any later digits are revealed. Once the puzzle ends, the app compares the player’s score to a theoretical best score, the highest total anyone could get if they’d been able to see all 25 digits ahead of time and arrange them perfectly.

To calculate that “perfect” score, the creators used a shortcut. They figured out the best possible arrangement for each group of matching digits separately, as if each group had the entire board to itself, then added up the results. The problem is that all those groups of digits actually have to share one single grid, and sometimes their ideal shapes simply cannot fit together at the same time. When that happens, the real best score is lower than what the shortcut predicts, because something has to give.

Take Day 88 of the game, which the authors use as their example. Their old method said the best possible score was 192 points. The actual best score, once properly calculated, was only 186. Players who thought they were six points away from perfection had actually already hit the ceiling.

How the Creators Uncovered the Truth

Fixing this meant treating each puzzle as a real math problem rather than eyeballing it. The pair turned to a method called integer programming, a technique that dates back to military logistics planning in the 1940s and is now used to solve complicated “what’s the best arrangement” problems by translating them into mathematical rules that specialized software can optimize. For a single Digit Party board, that meant setting up hundreds of variables representing every possible placement of every digit, then letting a computer search for the combination that scored the most points.

That approach works fine for checking one puzzle at a time, but Digit Party runs in a web browser and lets players generate unlimited random puzzles too. Running a full calculation every single time someone starts a new game wasn’t realistic. Instead, the creators figured out that what matters for scoring purposes isn’t which specific digits appear, but how many of each digit there are. A board with seven 3s and six 5s faces the exact same placement puzzle as a board with seven 5s and six 3s, just with different point values attached.

Using that insight, the creators boiled the problem down further: only the sizes of the digit groups matter, not the values. That leaves just 1,291 distinct size patterns for splitting 25 cells among at most nine digit groups. For most of them, 891 to be exact, their original shortcut actually gives the correct answer, because in those cases every digit group really can achieve its ideal shape at the same time without conflict. The remaining 400 patterns required extra work, calculating the trade-offs that happen when groups of digits compete for the same space on the board. Once all that math was done, the entire set of answers compressed down to a file smaller than three kilobytes, tiny enough to tuck into the game’s code so players’ phones never have to do any heavy lifting.

How Often Digit Party Actually Lied

With the correct method finally in hand, the creators went back and checked all three years of daily puzzles. Out of 1,096 total puzzles, 55 of them displayed an incorrect maximum score. Most of the errors were tiny. The typical mistake was just two points off, and the average discrepancy across all 55 puzzles was about 2.47 points.

A few stood out more. Day 88 held the record, with players told the max was 192 when it was really 186, a six-point gap. Day 813 tied that record, claiming a maximum of 187 when only 181 was achievable. The final mistake happened on Day 1095, just two days before the game’s three-year anniversary, and was off by three points.

Looking beyond the daily puzzles, the authors also checked every one of the roughly 13.8 million possible digit-count combinations that can arise in a 25-digit game. About 14.26 percent of them turned out to be flawed under the old shortcut, nearly three times the 5.02 percent error rate seen in the actual daily puzzles. The explanation comes down to how puzzles get generated: Digit Party’s daily boards draw 25 digits independently, which tends to favor more balanced mixes of digits. But the old shortcut is disproportionately likely to break down on uneven distributions, such as boards with many copies of just a few numbers. Since daily puzzles skew balanced, they dodge most of the trouble that shows up across the full range of mathematically possible boards.

An Unexpected Mathematical Bonus

Chasing down this scoring bug led the pair somewhere they didn’t expect. To understand how a single digit should ideally be arranged on a grid, they ran into a long-standing, unsolved geometry question about the best shape for a cluster of connected squares. Two other mathematicians had proposed an educated guess about the answer back in 2021. The Digi Party creators passed that guess along to a mathematician, who proved it correct in a 2024 paper. A puzzle game about matching digits, in other words, helped settle a real open question in mathematics.

A phone game fibbing about high scores sounds like a small thing, and for players chasing a personal best, it mostly was: most of the errors amounted to a point or two. But the story underneath it says something bigger about how tricky “simple” math problems can be. Figuring out the truly best way to arrange 25 digits on a grid required real computing power, a detour into an unrelated geometry puzzle, and three years before anyone even noticed something was off. The creators now say the game finally shows players the real number. Whether that makes those near-perfect percentages feel any different is up to each player to decide.