Connections gives AI a repeatable puzzle-solving test because every puzzle has the same 16-word, four-category structure.
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Semantic similarity alone cannot solve the game because words can be related through morphology, orthography, encyclopedic knowledge, association, or multiple meanings.
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A solver built from semantic graphs, graph neural networks, and reinforcement learning can reduce the search space and produce more explainable candidate solutions.
Summary
Shafik Quoraishee uses the New York Times Connections game to study how humans and AI solve word puzzles. The game presents 16 words that must be divided into four groups of four, with decoy relationships designed to mislead players and language models. He describes human play through fast intuitive System 1 thinking and slower deliberate System 2 reasoning. His computational approach models the board as a graph-coloring problem, then adds several kinds of semantic relationships. Relational alignment scores can be used to compare easier and harder puzzles, while distributions of puzzle categories can be tracked over time. Quoraishee also describes semantic graphs built from WordNet, ConceptNet, and word embeddings. A graph convolutional neural network proposes candidate subgraphs, and a reinforcement learning system helps select among them. The experiments are preliminary, and he wants to test the approach on more puzzles and connect it to the ARC-AGI benchmark.
Connections has a fixed structure that makes AI performance measurable
Quoraishee explains that Connections launched in beta in June 2023 and was officially released in August 2023. Each daily puzzle contains 16 words, which players must divide into four groups of four. Each word belongs to one group, and players can make up to four incorrect guesses. The categories also have a difficulty structure. Yellow is usually the most obvious, green requires more thought, blue often uses sayings, idioms, lexical links, or trivia, and purple tends to contain decoy overlaps. The fixed input and repeatable solutions make the game useful as a test bed for AI systems. He also stresses that the puzzles, mechanics, and programming are human-made.
Connections challenges language models because a solver must avoid being distracted by intentional decoys and superficial similarities. Quoraishee says that models have not reached a 100% solve rate across the game. A solution should also be explainable, since the difficult categories require reasoning about why words belong together. He shows ChatGPT producing a wrong solution and notes that model quality affects the result. The same puzzles can be played repeatedly, which allows systems to be compared on a reproducible input rather than on changing questions or private data. This makes Connections useful for examining how an AI reaches an answer, rather than only whether the final grouping is correct.
Human players combine intuition with deliberate reasoning
Quoraishee describes Connections through System 1 and System 2 thinking. System 1 is fast recognition, such as immediately seeing that two words share an obvious relationship. System 2 is slower reasoning, where a player searches their knowledge and weighs whether a word belongs to one possible group or another. Effective play uses both forms of thinking. Players can fail through either mode. They may trust an apparently obvious relationship that is a decoy, or they may think too deeply about a word that belongs to the obvious category. The game's difficulty comes from switching between quick pattern recognition and more careful analysis while the same word may support several plausible interpretations.
The board can be represented as an augmented graph-coloring problem
Quoraishee maps the 16 words to vertices in a graph and treats the hidden categories as four colors. The goal is to assign the same color to the four words in each category. Edges represent the strength of the perceived relationship between two words. This turns the puzzle into an augmented graph-coloring problem and gives an algorithm a structured search space. He mentions familiar graph-coloring methods such as backtracking and greedy coloring. Without relationship edges, a solver is left with a much harder task of sorting words randomly. The graph-coloring formulation also connects the puzzle to established computer science problems used in areas such as scheduling, frequency assignment, and wireless networks.
Semantic similarity alone misses the relationships that make puzzles difficult
Quoraishee argues that semantic similarity is insufficient because Connections uses several kinds of relationships. Words can be linked through anagrams and spelling, shared morphology, encyclopedic facts, or associations such as things that are red or green. A word can also have several meanings. He gives the example of "mole," which can refer to an animal, a birthmark, a spy, or a unit. Those multiple meanings can confuse both people and AI systems. A solver therefore needs more than one similarity score. It needs to compare how strongly words relate across different semantic dimensions, including cases where a relationship is indirect or based on a shared concept rather than a similar definition.
Relational alignment can compare puzzle difficulty
Quoraishee defines relational alignment as a score that measures how two words are associated under a chosen metric. He builds heat-map simulations that display these relationships and compares the overall alignment in easier and harder puzzles. In his examples, one hard puzzle has a solve rate of 19%, while an easier puzzle has a solve rate in the 70% range. The difference in alignment across categories suggests a computational way to estimate difficulty. He also describes time-varying alignment scores, which can be calculated across puzzles and plotted over time. A broken puzzle produces a zero in one example, showing that the metric can also expose unusual puzzle data.
Multiple semantic dimensions produce a richer puzzle model
Because two words can be related in several ways, Quoraishee treats relational alignment as a distribution rather than a single value. A radar chart can show how a word set relates through categories such as morphology, orthography, and encyclopedic association. He also builds a semantic distribution evaluation framework that counts categories across puzzles over time. The resulting distributions can be viewed as histograms or other trend data. Adding these relationships to the graph creates multidimensional structures, which he describes as hypergraphs. The model can distinguish intercluster strength, which measures connections between groups, from intracluster strength, which measures relationships within the groups found by the algorithm.
Graph neural networks and reinforcement learning generate candidate solutions
Quoraishee describes a graph convolutional neural network as the main solver for the geometric, multidimensional problem. It takes a graph as input and produces candidate subgraphs that might correspond to solutions. The system optimizes edge and node weights while testing which candidate graph fits the puzzle. A reinforcement learning component then helps traverse and select among the resulting subclusters. The full system combines machine learning agents with the graph-based representation. Quoraishee presents the approach as a way to make the solver's structure trackable and explainable instead of placing the puzzle directly into a language model and treating its reasoning as opaque.
The experiments are preliminary and need broader testing
Quoraishee reports that solvability improved on a small subset of hard puzzles after adding the graph-based components, although he describes the result as preliminary and says the work is still in progress. He wants to run the method on more puzzles and eventually connect it to game development. He is also concerned that language models may have seen Connections solutions on the internet during training, which makes their apparent solving ability difficult to interpret. The next steps include connecting the work to the ARC-AGI benchmark. His separation between this independent research and the New York Times' internal research is explicit, and he presents the project as an investigation rather than an authoritative evaluation.
"I'm actually trying to increase this intelligence space procedurally so that you can have a trackable and explainable way."15:29
Who should watch
You are building an AI solver for word puzzles and need a concrete way to represent decoys, ambiguous words, and category structure.
You want to compare puzzle difficulty with measurable features instead of relying only on solve rates.
You work on explainable AI and want an example that combines semantic graphs, graph neural networks, and reinforcement learning.
