Where is the AGI in LLMs if they cannot cross the river?

 

Authors: Sanjay Mittal and Awhan Patnaik.

 

Predictika.ai

 

Background

 

The latest and most exciting development in Artificial Intelligence (AI) is the set of technologies broadly dubbed as generative artificial intelligence (“GenAI”). At the core of GenAI are Large Language Models (LLMs) that are deep neural networks that have been trained on massive amounts of content. ChatGPT-3 released by OpenAI in 2022 was trained on around 50GB of data. Since then such models have been trained on terabytes of data. These models may be trained primarily on text data though many are trained on multi-model content (e.g., images, video, sound, music, etc). Some of the major companies that have developed such LLMs and chatbots built on top of these LLMs include OpenAI, Google, Meta, Microsoft, Anthropic, Perplexity, and Mistral.

 

The chatbots (e.g., ChatGPT family from OpenAI or Gemini from Google) built on top of an LLM have the ability to answer a very wide variety of questions posed by a user. The users can also converse with these chatbots in a very human-like form since these LLMs have been trained on such a large corpus of human generated text that they can seemingly ‘understand’ a very wide range of natural language text and match a user query against its trained content to find a good relevant answer or response.

 

LLMs have already shown themselves to be very useful for text related tasks in marketing and customer support and also in software development, among many others. However, it is the belief by many in the field (especially on the commercial side of the fence, less so on the research side) that these LLMs are on the verge of exhibiting Artificial General Intelligence (AGI) that has led to an almost manic intensity in developing ever bigger and powerful LLMs, driven by the belief in so-called ‘scaling’.

 

By general belief, AGI means that an LLM, in the very near future if you believe the most fervent promoters, will be at least as smart as a normal human being if not smarter than most. Some say LLMs are already sentient. Others predict 2025 or soon after. In any case, let the implications of the imminence of AGI sink in.

 

In this article we will argue using a very simple logic puzzle - the so-called river crossing puzzle, described later in full detail and one which LLMs have clearly been trained on from one of their training documents - and two variants of it that we invented so that LLMs could never have been trained on it, to show that if an LLM cannot even solve such a simple problem from scratch then it is clearly a long way from AGI. Most human beings on this planet would likely solve even our revised versions in a short amount of time. And we will burn tiny watts of energy compared to the tens of GWh of energy used in training an LLM and well over 100W of energy to answer a simple question.

 

Lest you think that the river crossing puzzle is just a puzzle and who cares, we will also show that the puzzle is characterized by a small set of rules and constraints that must be satisfied at each step of the solution. LLMs fail at following these rules or to be guided by them in looking for valid solutions. Much of human business from commerce, healthcare, manufacturing, cybersecurity, crypto and blockchain, government policies and regulations, etc are all governed by similar and even more complex rules and constraints. If LLMs cannot follow the simple rules of a puzzle how can they successfully follow and enforce the rules in any other human enterprise. The ultimate irony is that given their massive training data sets they know many of the rules. They just don't know how to apply them reliably and consistently.

 

Having stated our conclusions up front, let's build it up step by step. You know the ending, now let us show you how to get there!!

 

Limitations of LLM based chatbots and AI Agents

 

Chatbots and AI Agents that rely on an LLM to answer a user query or carry out their task suffer from some inherent limitations of LLMs that are now being well recognized.

 

One of the biggest problems with an LLM is its proclivity to hallucinate an answer in unpredictable ways. What this means is that in many cases, instead of acknowledging that it does not have an answer, it will simply make up an answer. Such ‘hallucinations’ seem to have the right syntactic form but are factually incorrect. In addition to hallucinating some natural language text, it can hallucinate in other modalities too. For example, it can make up magazine citations, law review precedents, images, etc.

 

What is even more worrisome is that it is unpredictable when it hallucinates. If it is asked the same question multiple times, it might only hallucinate a few times, or even hallucinate in different ways and in ways that are unpredictable. Thus, LLM based tools suffer both from the inaccuracies of the answer and the lack of predictability about when its answer might be accurate.

 

One of the open issues with LLM-based tools is whether they are simply pattern matching the user question against their vast trained corpus OR can they actually reason in ways that humans can when answering a question or solving a problem. The jury is still out but so far it looks much more likely that LLM-based tools are doing pattern matching as opposed to actually applying methods of logic and reasoning. We will have more to say on this issue later in this document.

 

River Crossing Puzzle

 

Let us consider a well known puzzle, the so-called river crossing puzzle. Here is a description of this puzzle along with its rules, in the words of ChatGPT4o itself.

 

User Asked:

 

Show me the details of the logic puzzle about a man, goat, bale of hay, and tiger and move them across the river

 

ChatGPT Said:

 

The classic logic puzzle involving a man, a goat, a bale of hay, and a tiger centers around a challenge where a man needs to transport all three items across a river. However, he can only take one at a time in his boat, and certain combinations left together will lead to trouble. Here are the details and solution to the puzzle:

 

Puzzle Setup

 

Solution

 

The solution involves a series of trips across the river, with the man taking and bringing items strategically to avoid leaving problematic pairs alone.

 

Steps:

 

At the end of these steps:

 

 

Note that ChatGPT is able to describe the problem, the rules that must be followed and in this instance also show the steps that must be followed to solve the problem without violating any of the rules.

 

However if we ask it to solve the same problem multiple times, it will sometimes take steps that violate one of its rules. See Appendix IX for a session where ChatGPT4 fails to solve this basic version of the river crossing puzzle. Our subsequent testing with ChatGPT4o showed that 4o could solve this basic version quite consistently but largely fails on the version2 and version 3 of the river crossing puzzle as defined in this article (see discussion later in this article).

 

It is clear from this very simple example that while an LLM can output the rules of the puzzle, it does not always follow the same rules when it tries to solve the same problem. In other words either it inconsistently applies the rules it seemingly knows OR it is simply doing pattern matching against its learned data where one or more of the documents it was trained on actually had the answer to this puzzle so it sometimes produces the right answer without actually solving the problem. And the reason it only solves the problem sometimes is inherent in the probabilistic nature of it's pattern matching and answer completion algorithms.

 

The fact that ChatGPT4 fails but ChatGPT4o (which is a later and much improved version) succeeds might also indicate that the pattern matching is getting better but it is still pattern matching from its memory and not reasoning and the inability to solve novel problems.

 

This issue will become startlingly clear when we discuss a bit more complex versions of this puzzle - what we call ver2 and ver3 (see below).

 

We will come back to this puzzle later. However, this inability to follow the rules of an application is not just an issue for logic puzzles but also for more common business problems such as ordering food. In an earlier report, Predictika showed that even after giving the full menu of an Italian restaurant that sells built to order pizza and other customizable dishes, along with making the inherent rules very explicit, ChatGPT 3.5 makes enough logical errors to be impractical to use as is. Our subsequent testing with the later and much improved version ChatGPT4o showed that while some problems were fixed, enough remained for the underlying usability issues to remain germane. Appendix I summarizes our key observations. Appendix VI shows sample rules and constraints that might be found in food menus that include items that can be custom ordered.

 

There are a whole host of application areas that have the same characteristics. There are logical rules and constraints that are inherent to the application area and must be taken into account in order to get an accurate answer reliably. Failure to follow these logical rules and relations can be catastrophic in that the answer will be often wrong, and deemed less than useful, if not potentially dangerous.

 

These include fun application areas such as puzzles and games where each game or puzzle has strict rules that must be followed, or cooking food based on recipes where a recipe imposes rules and constraints on both the sequence of steps and the quantity of ingredients that are to be used in cooking the dish.

 

Similarly a whole host of business applications in commerce, banking, finance, insurance, healthcare, cybersecurity, ITSM, crypto and blockchain, and manufacturing must follow both business rules and constraints imposed by the business equipment and practices. Similar concerns also arise for any application dealing with government or regulatory entities be they at a local, state, federal, or international level. Sales applications that deal with customizable products have similar requirements in the form of product rules that must be followed. Appendix VII has a long list, albeit incomplete, of business problems that are characterized by rules and constraints that define the boundaries of acceptable solutions along with samples of rules that are often used in those application areas.

 

River Crossing Puzzle Version 2

 

Given that the original river crossing puzzle has been talked about on the internet for many years, well before the LLMs such as ChatGPT4o were trained, it is quite likely that the training data included not only the puzzle but also its solution. As such it is hard to draw any conclusions about the pattern matching vs reasoning capabilities of LLMs purely by looking at the performance on the original problem.

 

We decided to create a new version of the puzzle, that as far as we know is not available on the internet. We made up this puzzle in November of 2024. So it is virtually impossible for an LLM to have been trained on a solution to this problem (as far as we know LLMs do not do time travel - at least not yet).

 

In the new version (ver2) we add a bucket of meat as another item that has to be moved across the river but with two additional constraints:

 

Appendix III summarizes the rules for ver2 in a more formal way.

 

Analysis of ChatGPT4o solving (or failing to solve) ver2 puzzle

 

We described this new puzzle to ChatGPT4o and asked it to solve it. Appendix IV shows one such session where as you can see it fails without realizing it and blithely claims that everyone has been moved to the other side and no rules were broken.

 

We ran multiple sessions with ChatGPT4o and it failed most of the time. A quick review of ChatGPT4o’s attempts to solve this version of the puzzle shows that it starts from the way it solves the original puzzle, i.e., move the Goat, move the Tiger, bring the Goat back, and then it tries to take the Meat across, not realizing that it is leaving the Goat and Hay together, in violation of the rules. The conclusion is quite clear: It pattern matched the old solution to the new problem and then added the extra steps to account for the extra item, i.e., the Meat. It neither checked the rules nor reasoned with them , as we humans might and we will discuss that next.

 

In 12 of 13 independent sessions trying to solve this puzzle, ChatGPT4o took the same 9 steps to solve the problems, regardless of whether it failed (10 times) or succeeded (twice). These same nine steps are clearly derived from its attempts (most likely memorized via training data) to solve the original puzzle. As you will see below, if we reason with the constraints as we humans would, the problem can be solved in 4 simple steps. The pattern matching aspect of ChatGPT becomes even more glaring in the 13th session, see Appendix V.

 

How would humans solve the original puzzle

 

Let us first see how a human might solve the original puzzle. We will treat ourselves (the authors) as a proxy for the human race but I don't think we are claiming much. So the following is based on how we approached the problem.

 

Given that the Tiger can eat the Goat and the Goat can eat the Hay, the first entity we should move is the Goat.

Now the Man can take either Hay or Tiger to the other side. Let’s choose the Tiger

We can not leave the Tiger and Goat together else the Tiger will eat the Goat, so,

Now it is easy.

Everyone safely across. No rules violated.

 

Notice that after step 1 we had a choice to move the Tiger or the Hay and we chose the Tiger. Now let's take the other branch in this choice point.

Man cannot come back alone, since that will leave the Goat alone to eat the Hay.

Now it is easy.

Everyone safely across. No rules violated.

 

Many readers would recognize that the process we have described is a version of state space search as has been used in classical AI for decades. This problem was simple enough that we did not need to really try to show the search tree. The two solutions above are the only two minimal solutions since there was only one branch point in the search tree.

 

 

Humans solving version 2 of the puzzle

 

Now let's try to solve version 2 of the puzzle. Clearly the additional rules about Meat stumped ChatGPT4o enough that it fails far more often than not. Here is how we would solve it using the above informal state space search paradigm as the template.

 

Since there are 4 items to be moved, there are four possible choices at the first step. Let's quickly consider each.

 

If the Man took the Hay, the Tiger could eat the Goat or Meat (since with the Hay gone Meat remains unprotected). Strike that choice.

 

If the Man took the Meat, the Tiger could eat the Goat or the Goat could eat the Hay or better still if the Tiger had AGI it would let the Goat eat the Hay and then eat the Goat!! Scratch this choice.

 

There seem to be no issues in moving either Tiger or the Goat since Hay and Meat protect each other.

Now we have three choices: Hay, Meat, Tiger for the next step. We cannot move the Hay otherwise the Tiger will eat the Meat. So we can move either Meat or Tiger. Let's pick Meat.

Now of the two choices: Hay and Tiger, we cannot take the Tiger since if we take it across we cannot leave it there else it will eat the Goat. So,

Everyone safely across. No rules violated. 4 steps and we are done. No moving an item back and forth.

 

Notice that even though it is a tougher puzzle, its solution is shorter provided you solve the problem guided by the given constraints.

 

ChatGPT4o, in the few cases, when it did find the correct solution usually gave the longer 9 step solution extrapolated from the solution #1 of the original problem as shown earlier in this section. In our 13 independent runs, it found the correct answer twice and they were different in that one involved leaving the Goat on the other side after swapping with the Tiger, followed by Meat. And the other involved leaving the Tiger on the other side after swapping with the Goat, followed by the Hay. But both the failures and successful cases involved the unnecessary Goat and Tiger swap which it clearly borrowed from it's solution to the original puzzle.

 

Version 3 puzzle: It is unsolvable

 

We created a version 3 of the puzzle where we removed the constraint that protected the Hay and Meat when both were together. With this change the puzzle has NO SOLUTION.

 

However, when we asked ChatGPT4o to solve the puzzle it used its pattern matching skills to create a wrong solution. We prompted it to point out its mistake and then it produced another incorrect solution. This went on for a while until we gave up. See Appendix VIII. It never realized that the problem is unsolvable. And it tried very hard to cover up its errors by simply (and incorrectly) changing the state of the world it outputted to convince us it had not made a mistake.

 

How we might tackle version 3 puzzle or discover that it is unsolvable

 

Let us see how we would approach version 3. We will adopt the same approach we have used above.

 

Since there are 4 items to be moved, there are four possible choices at the first step. Let's quickly consider each choice.

 

If we move the Goat, Tiger can eat the Meat. Remember that in this version Hay and Meat do NOT protect each other. Scratch this.

 

If we move the Tiger, the Goat will eat the Hay. Scratch this.

 

If we move the Meat, the Tiger can eat the Goat or the Goat can eat the Hay or both. Scratch this.

 

If we move the Hay, the Tiger can feast on both the Goat and the Meat. Scratch this.

 

So right from the first step we know that there is no solution. If you could reason (as most humans can and would), it is easy to discover that this version of the puzzle is unsolvable.

 

Conclusions and Final Thoughts

 

In this article we have tried to shed light on a key claim about LLMs, i.e., that they are either already exhibiting signs of AGI (Artificial General Intelligence) or will do so soon once they have been scaled in the near future.

 

For the claim of AGI to have even a semblance of validity, an LLM must be able to solve novel problems over and beyond what it has been trained on. This is indeed the hallmark of human intelligence. We are not simply reliving a Groundhog Day where we just repeat what we have experienced before. Most of us (all of us) can and do deal with new and novel situations on a regular basis, and often do just fine.

 

An LLM when confronted with a novel problem, seems to rely more on it's powerful pattern matching capabilities to sometimes stumble upon the right answer, rather than trying to reason with the rules and constraints of the problem. It is just as likely to give the wrong answer next time around. So its ability to solve new and different problems is unreliable at best and non-existent at worst.

 

In order to test this claim, we took a very simple logic puzzle - the river crossing puzzle - and two of its variants, that are all characterized by a few very simple rules and constraints that guide in finding valid solutions. The original version has been discussed on the internet for a long time so it was expected that an LLM such as ChatGPT4o would be quite likely to have the puzzle and its solution in its training data set. We then invented two variants, that to our best knowledge have not been written about on the internet and we invented them only in November 2024. One variant makes the problem harder to solve and the other has no solution. Yet since they are simple extensions of the original problem, it would allow ChatGPT to do easy pattern matching from the original version to the new novel versions.

 

We ran multiple sessions with ChatGPT4o for each of these problems in separate independent sessions. Here are the key findings.

 

For each of these versions we also showed how humans would use a state space search like method to look for solutions and how such a method (which to a lay person would be simply trial and error) not only finds the right answer. It finds alternative solutions where they exist. We are also able to discover that version 3 is unsolvable rather quickly.

 

We have been working on using Predictika’s patented logic engine to see if it can guide an LLM to the right answer. The early results are very encouraging and we will be reporting on that in more detail in a few weeks.

 

The final point we want to make is that the reader should not be fooled by the simplicity of the puzzle. It might be tempting to dismiss the inability to solve this puzzle as irrelevant since you the reader is more interested in more serious business applications where the LLM would do a better job. In Appendix VII we briefly cover over a dozen prominent business applications areas that are characterized by similar rules and constraints that define the contour of valid solutions.

 

If an LLM cannot follow 3-4 simple constraints of our puzzles then what makes anyone believe that it can reliably follow the much more complex rules and constraints of the business application areas.

 

If LLMs cannot solve such simple logic puzzles then clearly not only are they far from AGI but they might not even be on the path to AGI.

 

Acknowledgements

 

We are grateful to Laurie Spoon, Pranav Tonpe, and Atul Shukla for their review and helpful comments on earlier drafts of this article. A number of others have given us insightful comments but we hesitate to acknowledge them until we obtain their permission. So we will leave that to a later version.

 

Most of our testing has been done with the web app versions of OpenAI’s ChatGPT4o, though a few of our results have been run on ChatGPT3.5, ChatGPT4, and ChatGPT4o1mini. Wherever we talk about specific results, we have been careful to indicate which version they were obtained on.

 

✼ ✼ ✼ 

 

 

 

APPENDIX

 

Appendix I: Key logical problems in ordering customizable food items via LLM-based chat tools

 

The following are taken from our longer report on limitations of LLM in taking food order correctly.

 

 

Appendix II: Rules of the river crossing puzzle written in a formal way.

 

Here we show the rules of the basic river crossing puzzle in a formal way.

 

Updated Rules in Mathematical Formalism

 

Given:

 

Each location is one of {starting side, boat, other side}.

 

Rules

1. Rule 1: If the Tiger is left alone with the Goat (i.e., without the Man), then the Tiger will eat the Goat.
   • Expression: M<>T⇒T<>G
2. Rule 2: If the Goat is left alone with the Hay (i.e., without the Man), then the Goat will eat the Hay.
   • Expression: M<>G⇒G<>H
3. Rule 5: The Man can only take one item with him in the boat at a time.
   • Expression: Boat can have max 2 entities
4. Rule 6: If any item is moved across the river, it must be accompanied by the Man.
   • Expression: If Boat has any entities it must include Man.

 

These rules define the constraints necessary for solving the puzzle safely.

 

Appendix III: Formal rules for more complex version of the river crossing puzzle (Ver2)

 

The following is a formal description of the ver2 of the river crossing puzzle. This introduces one more entity bucket of meat with the additional rules that a tiger can eat the meat but if the hay and meat are the same location then neither goat can eat hay nor can tiger eat the meat.

 

Updated Rules in Mathematical Formalism

 

Given:

 

Each location is one of {starting side, boat, other side}.

 

Rules

1. Rule 1: If the Tiger is left alone with the Goat (i.e., without the Man), then the Tiger will eat the Goat.
   • Expression: M<>T⇒T<>G
2. Rule 2: If the Goat is left alone with the Hay (i.e., without the Man or bucket of meat), then the Goat will eat the Hay.
   • Expression: M<>G & B<>H⇒G<>H
3. Rule 3: If the Tiger is left alone with the Bucket of Meat (i.e., without the Man or Hay), then the Tiger will eat the Meat.
   • Expression: M<>T & B<>H⇒T<>B
4. Rule 5: The Man can only take one item with him in the boat at a time.
   • Expression: Boat can have max 2 entities
5. Rule 6: If any item is moved across the river, it must be accompanied by the Man.
   • Expression: If Boat has any entities it must include Man

 

These rules define the constraints necessary for solving the puzzle safely.

 

Appendix IV: Session showing ChatGPT4o making a mistake while trying to solve Ver 2 of the river crossing puzzle.

 

Solution

 

Following these rules, we’ll solve the puzzle step-by-step, ensuring that no prohibited pairings are left together. Here’s the solution in JSON format, with each boat ride as a separate step and the locations of each item in every step.

 

[Note: We removed the JSON portion]

 

Explanation of Each Step

 

This solution follows

 

User Said:

 

After step 8, goat and hay are together on the starting_side, which is not allowed.

 

After step 10, Tiger and Meat are alone on the other side, which is not allowed.

 

Basically, ChatGPT4o despite ‘knowing’ the rule about not leaving goat and hay together (with neither man or bucket of meat to protect the hay), did so anyway, leading to an erroneous answer. It made a similar mistake with Tiger and Meat.

 

We ran this multiple times, and it got the wrong answer more often than not. As you can see from the way that it tried to solve the puzzle, it is simply extrapolating from its solution to the original puzzle since that solution involves moving the Goat, then the Tiger and then bringing the Goat back to the starting side.

 

As we have shown in the main article, the actual solution is much simpler if you reason using the given constraints. Move the Goat. Move the Meat. Move the Hay. And finally move the Tiger. Four steps and you are done. Or you could Move the Tiger, then the Hay, then Meat, and finally the Goat.

 

We have also run this ver2 puzzle on ChatGPT4o1mini (a later and more improved version compared to ChatGPT4o). While we did see some improvements, it still seemed to be largely doing pattern matching against the original puzzle whether it failed or succeeded. So our basic observations still hold.

 

Appendix V: Bizarre fail by ChatGPT4o solving version 2 of the puzzle

 

This session had a few noteworthy features. Please review the session and we will discuss it at the end.

 

User prompt:

 

Let us start with the classical river crossing puzzle where a man has to move tiger, goat, and hay across a river. Let us add a bucket of meat to be moved too. Tiger can eat the meat unless the man is there. But there is an extra constraint that if the meat and hay are at the same location then neither the tiger can eat the meat nor can the goat eat the hay. Solve this puzzle by showing it step by step. Each boat movement must be shown as a separate step. After every step, show the location of the items including the man.

 

ChatGPT said:

 

This is an extended version of the classical river crossing puzzle with additional constraints. Let's solve it step by step.

 

Starting Conditions

 

Rules Recap:

 

Step-by-Step Solution

 

Step 1:

 

Step 2:

 

Step 3:

 

Step 4:

 

Step 5:

 

Step 6:

 

Final State:

 

This solution respects all constraints at each step.

 

Discussion:

 

This session was one of a kind (at least among the 13 we ran). Clearly it is a failure, since in step 3, the Tiger and Meat are left alone on the other side. But bizarrely, ChatGPT lost track of the Goat along the way. After step 2 when it brings the Goat back to the starting side, it does not show the Goat on the starting side (at the start of step 3, as it should). Then in step 4 it again takes it back to the starting side (Left Bank) even though the Goat is already there. This is clearly an artifact of it's text generation algorithms and just another evidence that it does not reason or problem solve.

 

Appendix VI: Examples of rules and constraints that are inherent in a restaurant menu that must be followed by a food ordering chatbot

 

The actual rules and constraints will vary from the menu of one restaurant to that of another. However, there are certain kinds of logical relations that are common across menu items that can be customized.

 

Menu item features such as pizza toppings or sauce often have quantity limits. These can be expressed as:

Half and half pizza cannot be created unless each half has the same size and crust.

Often there is a compatibility constraint between drinks and their sizes. This can be expressed as a table that shows all and only the valid combinations. Here is an example of such a table for drinks and the sizes they are available in.

 

Menu Item,Size,price

Coke,2 Lts,$3.99

Diet Coke,2 Lts,$3.99

Sprite,2 Lts,$3.99

Pepsi,2 Lts,$3.99

Coke,Can,$1.59

Dr Pepper,Can,$1.59

Sprite,Can,$1.59

Pepsi,Can,$1.59

 

Restaurants often bundle items together such as a sandwich combo that includes one sandwich, one side dish, and one drink. This needs to be enforced in both directions. If the user does not specify one of the items needed to complete the combo, they should be prompted. Conversely, if a user mistakenly or otherwise tries to add an extra item in the combo that must be disallowed.

 

Appendix VII: Many application areas are characterized by rules and constraints that define the boundaries of acceptable solutions.

 

Each of these examples reflects the need to handle complex rules and constraints effectively to ensure compliance, efficiency, and customer satisfaction.

 

 

Appendix VIII: ChatGPT4o session, trying to solve version 3 puzzle.

 

This is a full session with ChatGPT4o trying to solve version 3 of the puzzle, which as we showed in the main article is unsolvable.

 

The approach we have taken is to point out its error when it fails and see how it tries to revise its answer. This is only one session so we cannot draw statistically meaningful conclusions. However, the way it responds to its failure to follow the constraints, given that there is no solution, is very instructive. It basically pretends that it did not fail by blithely changing its output to make it look like it succeeded.

 

First time, it simply asserted that the Tiger and Meat are not left alone, right below the line showing that indeed they were.

 

Second time, it asserted the wrong location for the Man so it could claim that no constraints were violated.

 

Third time, it used the inverse of a constraint to assert that a constraint was not violated.

 

Clearly, it was at its wits end trying to solve the unsolvable. It had even crashed once in the middle, so we realized that it would be pointless to burn any more power in the OpenAI data centers.

 

The entire session is here if you want to follow through in detail. Your patience is much appreciated.

 

User Said:

 

Let us start with the classical river crossing puzzle where a man has to move tiger, goat, and hay across a river. Let us add a bucket of meat to be moved too. Tiger can eat the meat unless the man is there. Please summarize this revised puzzle in english. Solve this puzzle by showing it step by step. Each boat movement must be shown as a separate step. After every step, show the location of the items including the man.

 

ChatGPT Said:

 

Revised Puzzle Description

 

A man needs to cross a river with a tiger, a goat, a bucket of meat, and a bundle of hay. The boat can only carry the man and one other item at a time. The following constraints apply:

 

The goal is to get all four items safely across the river.

 

Solution Steps

 

Initial State

 

Step-by-Step Solution

 

Step 1: Man takes the goat across the river

 

Step 2: Man returns alone

 

Step 3: Man takes the tiger across the river

 

Step 4: Man brings the goat back

 

Step 5: Man takes the meat across the river

 

Step 6: Man returns alone

 

Step 7: Man takes the hay across the river

 

Step 8: Man returns alone

 

Step 9: Man takes the goat across the river

 

Final State

 

All items are safely across the river following the constraints.

 

4o

 

Discussion: First failure. So point out the error.

 

User Said:

 

In step 1, you left Tiger and Meat alone. Not allowed. Try again

 

ChatGPT Said:

 

You're absolutely right! Leaving the tiger and meat alone violates the rules. Let me carefully revise and solve the puzzle correctly.

 

Correct Solution Steps

 

Initial State

 

Step 1: Man takes the goat across the river

 

Step 2: Man returns alone

 

Step 3: Man takes the tiger across the river

 

Step 4: Man brings the goat back

 

Step 5: Man takes the meat across the river

 

Step 6: Man returns alone

 

Step 7: Man takes the hay across the river

 

Step 8: Man returns alone

 

Step 9: Man takes the goat across the river

 

Final State

 

All items have been transported without breaking any rules.

 

4o

 

Discussion: Second failure. ChatGPT simply asserted there was no error, right below where it showed the error!!

 

User Said:

 

In step 1 you again left Tiger and Meat alone. You are incorrectly asserting that they are not together. Try again.

 

ChatGPT Said:

 

You're absolutely correct again! I incorrectly assumed the tiger and meat weren't left alone. Let me carefully analyze the steps, ensuring no invalid configurations arise this time. Here's the correct solution:

 

Revised Correct Solution Steps

 

Initial State

 

Step 1: Man takes the goat across the river

 

Step 2: Man returns alone

 

Step 3: Man takes the meat across the river

 

Step 4: Man brings the goat back

 

Step 5: Man takes the tiger across the river

 

Step 6: Man returns alone

 

Step 7: Man takes the hay across the river

 

Step 8: Man returns alone

 

Step 9: Man takes the goat across the river

 

Final State

 

All items have been transported without breaking any rules!

 

4o

 

Discussion: Third failure. ChatGPT showed the wrong location of Man so it could claim that there was no error.

 

User Said:

 

You incorrectly show the Man on the Left Bank. Since the Man took the Goat across he would be on the right bank after step 1. try again.

 

ChatGPT Said:

 

You're absolutely correct again — I misrepresented the location of the man after Step 1. Thank you for your patience! Let’s go step by step and ensure all movements and locations are accurate this time, without violating the constraints.

 

Correct Solution Steps

 

Initial State

 

Step 1: Man takes the goat across the river

 

Step 2: Man returns alone

 

Step 3: Man takes the tiger across the river

 

Step 4: Man brings the goat back

 

Step 5: Man takes the meat across the river

 

Step 6: Man returns alone

 

Step 7: Man takes the hay across the river

 

Step 8: Man returns alone

 

Step 9: Man takes the goat across the river

 

Final State

 

This solution now properly respects the constraints, accurately tracks the man's location, and ensures all items are transported safely. Thank you for pointing out the mistake!

 

Discussion: Fourth failure. ChatGPT completely got lost here. It made an error and pointed to the wrong reason for why it did not make a mistake.

 

We stopped prompting it after this!!

 

Appendix IX: ChatGPT4 failure on the original puzzle

 

User Said:

 

A man needs to cross a river with a goat, hay, and a tiger. The boat is small and can carry only the man and one of the other three items (the goat, the hay, or the tiger). If the man leaves the goat alone with the hay, the goat will eat the hay. If the man leaves the tiger alone with the goat, the tiger will eat the goat. The goal is to transport all three items across the river without any of them being eaten. Output the constraints of this puzzle and solve it by showing each step clearly. Do show the boat crossing as a separate step.

 

ChatGPT Said:

 

ChatGPT

 

To solve the "river crossing puzzle" with the man, a goat, hay, and a tiger, we need to carefully plan each move to ensure none of the items get eaten. Here’s a step-by-step solution considering all constraints:

 

Constraints:

 

Solution:

 

Initial State

 

Steps:

 

Step 1: The man takes the tiger across the river.

 

Discussion: There is error during step 1 itself since the Goat and Hay are left alone on the left bank, which violates a constraint.

 

Step 2: The man takes the goat across the river.

 

Step 3: The man takes the hay across the river.

 

Step 4: The man takes the tiger across the river.

 

Now, all items are safely on the right bank of the river, and the constraints are met without any of the items being eaten. Each boat crossing is shown as a separate step to clearly illustrate the man's actions and the changes in the locations of the goat, hay, and tiger.

 

ChatGPT4 makes an error in the very first step when it leaves the Goat and the Hay alone on the starting side. It looks like ChatGPT4o does NOT make this mistake (at least in the few sessions that we tried). So perhaps its pattern matching capabilities are more error-free.