Sudoku is too difficult for artificial intelligence. “AI does not think logically, but determines solutions based on probability”

Numerical puzzles such as Sudoku are too complicated for artificial intelligence (AI) – scientists have determined. The machine's even greater problem is explained by how they found a solution.

Numerical puzzles are entertainment known for millennia – the first appeared in ancient China, in the newspapers they began to be published at the end of the 19th century OK. 20 years ago, Sudoku, a puzzle, first printed in 1986 in the Japanese magazine “Nicoli” for the first time in 1986. Today, this game has millions of lovers in the world, only different versions of the application for mobile devices have been downloaded by about 200 million users.

Sudoku consists in filling with numbers of empty square fields of the 9×9 board. Each line, column and 3×3 square (so -called numerical block), into which the board is divided, must contain one digit from 1 to 9, the numbers cannot repeat in them. Mathematicians from the University of Sheffield (Great Britain) proved in 2005 that There are about 6 trillions of all possible Sudoku boards (6 x 10 to 21 power). There are other versions of this game – for example, the 6×6 board must be filled with numbers from 1 to 6.

Now it turned out that Sudoku is a challenge for artificial intelligence. Although AI is making great progress, among others In the analysis of large data sets, generating texts, images and films or translations, logical tasks are its weak point. This was confirmed by scientists from the University of Colorado at Boulder (USA), whose article on this subject appeared in the “ACL Anthology” – a collection of over 110,000. work collected by the Association for Computational Linguistics, ACL).

As the main author of the work said, an expert in the field of computer science and machine learning Aniarudh Maiya, Sudoku solving has several important elements. – You have to proceed step by step, constantly evaluate numerical fields and consistently follow the rules. Puzzles of this type are fun, but they are also an ideal microcosm for testing the decision -making process in machine learning – explained the expert.

As part of the Maiya study and his team, they created 2300 Sudoku with varying degrees of difficulty in the 6×6 fields. Their solution scientists commissioned several large language models (LLM), including O1, Llama-3.1, Gemma-2 and Mistral.

The experiment showed that For all AI models, the command was too difficult – in total they managed to solve 0.4 percent. boards. Researchers attribute this to the fact that artificial intelligence does not think logically, but determines solutions based on probability. That is why tasks based on rules and reasoning are difficult for her. – Models of artificial intelligence have problems taking into account at the same time all limiting factors in the numerical net – the authors of the work explained.

O1, which solved about 65 percent, was the best among the LLM respondents. Sudoku board. However, with the increase in the degree of difficulty of the puzzle, its effectiveness indicator also dropped.

Even more problems arose when scientists ordered AI to explain how she reached the solution of the puzzle. All tested models only in 5 percent cases were able to correctly justify entering specific numbers. Often, the answers were incorrect or unclear. – For example, AI said: here there can be two, because there are two in this poem, which was not true – said the co -author of the study Dr. Ashutosh Trivedi.

He added that in some situations, artificial intelligence ignored the combinations of numbers on the board or invented absurd justifications. In one such case, during a conversation about Sudok, one of the models suddenly gave the weather forecast. “AI was completely confused and reacted in a strange way,” said Dr. Trivedi.

According to the authors, the results of the study show that despite the impressive achievements of artificial intelligence, it cannot be fully relying on it, especially in tasks requiring precise reasoning. – Many people talk about new skills of AI models that could not be expected. However, it is not surprising that he is still doing poorly in many tasks – he summed up Ania Maiya. (PAP)

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