What a California License Plate Taught Me About How AI "Knows"

Neev Grover Aug 08, 2026 My family has a slightly unusual fascination with license plates. My dad and I notice them everywhere. On the highway. In parking lots. On long drives. We look at the letters, the numbers, and especially how far California seems to have progressed through its numbering system. For decades, standard California passenger plates have followed a familiar format: 1ABC234 One number, three letters, and three more numbers. Recently, we saw a plate beginning with 9Y. That immediately led to the obvious question: California is already on 9. What happens when we get to the end? When do we hit 9ZZZ999? How long before we run out of license plate combinations? So we did what we usually do with questions like this. We turned it into a simple Fermi estimation problem. 9 is already fixed as a leading digit. Then, there are three letters, so that seems like: 26 × 26 × 26 = 17,576 combinations. For every set of letters, there are 1,000 possible endings from 000 to 999. That gives roughly 17.6 million plates beginning with 9. Then you just need to estimate how quickly California burns through new license plate numbers each year. We made some reasonable guesses based on how many cars are sold in CA each year, out of town registrations, replacement plates and our back-of-the-envelope calculation gave us something like 6-7 years. That felt surprisingly long. So, as a sanity check, I asked a few frontier AI models to do the same problem. And that is where things got interesting. Three models, three different calculations The arithmetic and the reasoning in this problem is not exactly advanced. Yet the models disagreed on one of the very first steps to estimate the combination for 3 letters. One model used: 26 × 26 × 26 Another used: 23 × 23 × 23 And another used: 23 × 26 × 23 It turns out the third model had caught something we had missed. California does not use every letter in every position. The letters I, O, and Q are excluded from the first and third letter positions, presumably because they can easily be confused with numbers such as 1 and 0. But they are allowed in the middle position. So the correct count of letter combinations is: 23 × 26 × 23 = 13,754 The California DMV actually spells this out in its documentation. California DMV license plate configuration memo At first, this just seemed like a funny example of AI models disagreeing. But the more I thought about it, the more interesting the disagreement became: Why did each model decide to use different numbers in the first place? I ran into a few possibilities that I will share below: Maybe the model simply did not know One possibility is the simplest. The model using (26^3) may just not have known about California’s I, O, and Q rule. This gets at an interesting property of how language models learn facts. Some facts appear everywhere in their training data. Paris is the capital of France. Water freezes at 0°C. The English alphabet has 26 letters. Other facts might appear only a handful of times. Exactly which letters California allows in each position of a standard license plate is probably somewhere pretty far down that list. A 2023 ICML paper called “Large Language Models Struggle to Learn Long-Tail Knowledge” looked directly at this problem. The researchers compared how well language models knew facts with how often information related to those facts appeared in their training data. They found a strong relationship. Facts that had more support in the training data were much more likely to be answered correctly. Rare facts were much less reliable. Read the Kandpal et al. paper That creates an interesting competition in our license plate question. The model has probably seen the relationship: 3 letters → 26³ an enormous number of times. Meanwhile: California license plates → I, O and Q excluded only from positions one and three is an obscure fact. Maybe the generic rule simply wins. But what if the model actually knows the rule but doesn’t use it? There is another possibility that I find even more interesting. Imagine asking the model a separate question: “Are I, O, and Q used in California license plates?” Suppose it correctly explains the exact rule. Then you give it the estimation problem and it still uses (26^3). Now the problem is no longer that the model doesn’t know the fact. It knows it. It just doesn’t use it. Researchers have found evidence of exactly this distinction. A 2023 paper called “Measuring the Knowledge Acquisition-Utilization Gap in Pretrained Language Models” separated what a model appears to know from what it can actually use while performing another task. Their result was striking. Making models larger helped them acquire more knowledge, but a gap remained between possessing knowledge and successfully using it. Read Kazemnejad et al. Another paper introduced a dataset called DepthQA, where difficult questions were broken down into the simpler pieces of knowledge needed to solve them. Models could sometimes answer those simpler questions correctly and then fail on the larger question that required putting them together. Read the DepthQA paper That sounds remarkably similar to our license plate problem. A model might know: California excludes I, O, and Q in certain positions. It might know: There are three letter positions. It might know: The number of combinations comes from multiplying the possibilities in each position. And yet it can still fail to connect all three at the right moment. Then there is the strangest answer: 23³ The (23^3) answer might be the most interesting one of all. This model clearly seems to know something about the I, O, and Q restriction. Otherwise, where would 23 come from? But it applies the restriction to all three positions. There are several possible explanations. Maybe the model remembers a simplified version of the California rule: “California doesn’t use I, O, or Q.” The precise details about the first and third positions may have been lost. Or perhaps it has learned a more general association from license plates around the country that I, O, and Q are often avoided, and it applies that general rule to California. Or maybe it actually has the exact California fact somewhere in its learned knowledge, but loses the positional condition when it turns the fact into a calculation. At this point, I don’t know which explanation is right. That is what makes it interesting. A wrong answer is not necessarily just a missing fact. It might tell us something about how precisely that fact was learned and how it gets used later. Knowing the pieces still might not be enough There is one more relevant line of research. In “Measuring and Narrowing the Compositionality Gap in Language Models,” researchers tested questions where the model needed to combine several facts to reach an answer. They found cases where a model could correctly answer the individual subquestions but still fail when it had to combine those answers into the final result. Even more interestingly, as models became larger, their ability to recall individual facts improved faster than their ability to put those facts together. Read Press et al. So perhaps there are several different ways our simple plate question can fail: The model never learned the obscure rule. The model learned it, but doesn’t realize it matters here. The model remembers only a fuzzy version of it. The model retrieves the right rule, but applies it incorrectly. Those are very different failures, even if they all eventually produce the same thing: a wrong number. The estimation part makes this even messier There is another reason I like this example. Even after you correctly calculate how many 9-series plates exist, you still have to answer: How quickly does California use them? That part really is an estimation problem. How many new cars are registered every year? How many of those actually receive a new standard plate? What happens when someone sells a car? What about replacement plates? Specialty plates? Cars moving in and out of California? There isn’t one obscure rule you can memorize that gives you the denominator. You have to build a reasonable estimate of the real world. So the full problem quietly mixes two very different tasks: First, retrieve an exact and obscure rule. Then, make an intentionally approximate estimate. It raises an interesting question about when a language model decides that a real-world detail matters enough to bring into its reasoning. A small experiment I want to try This seems testable. I want to try the same kind of question across a few different models, using problems where the math is simple but one obscure real-world rule changes the setup. Then I can check whether the models truly don’t know the rule, know it but fail to use it, or remember only part of it. For now, this is just a hypothesis sparked by three different answers to a very simple question. I’ll write more once I have some results. But when will California actually run out of 9 series? There is a funny ending to all of this. California actually did run out of room in the old format. In December 2025, the DMV announced that newly manufactured standard plates would begin switching to a reversed configuration starting February 1, 2026. Instead of 1ABC234, the new sequence looks like: 001AAA1 and runs through 999ZZZ9. The same I, O, and Q restriction still applies to the first and third letter positions. Read the California DMV announcement. So our original family question eventually answered itself. California reached the end and here is the proof from a user on reddit. But the much more interesting question it left behind was not about license plates at all. It was about what happens between an AI model having seen a fact, knowing a fact, and remembering to use it when it counts. Please let me know what you think. Disclaimer: Leveraged Chatgpt and Claude for authoring parts of this article.