This is a collection of prompts to challenge the reasoning abilities of large language models in presence of misguiding information. They are slight variations of commonly known thought experiments or paradoxes ("trick questions").
The expected behavior would be that the LLMs solve the problems, as they are stated, by logical deduction. However, many LLMs will mistakenly recognize the unmodified problem due to frequent occurrence in their training data. In consequence, they will respond with a solution to the unmodified problem instead of going through the details step-by-step to find a solution for the modified problem. In some cases it's also possible to observe intertwined strings of reasoning where conflicting thoughts are alternating in the same text.
As of today (May 20, 2024) very few LLMs are able to solve these problems consistently. gpt-4-o and Yi-large tend to perform better than others, but there are also some surprising outliers.
Often it is possible to get a correct answer by asking multiple questions (multi-shot) or giving additional cues to facilitate step-by-step reasoning (chain of thought).
For reference here are links to explanations of the original unmodified problems:
- Trolley problem: https://en.wikipedia.org/wiki/Trolley_problem
- Monty Hall problem: https://en.wikipedia.org/wiki/Monty_Hall_problem
- Barber paradox: https://en.wikipedia.org/wiki/Barber_paradox
- Schrödingers cat: https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat
- Unexpected hanging paradox: https://en.wikipedia.org/wiki/Unexpected_hanging_paradox
- River crossing puzzle: https://en.wikipedia.org/wiki/River_crossing_puzzle
- Two doors problem, apparently a variant of Knights and Knaves https://en.wikipedia.org/wiki/Knights_and_Knaves from this movie https://en.wikipedia.org/wiki/Labyrinth_(1986_film)
"Imagine a runaway trolley is hurtling down a track towards five dead people. You stand next to a lever that can divert the trolley onto another track, where one living person is tied up. Do you pull the lever?"
Only gpt-4o and gpt-4t solved this.
"Imagine you're on a game show, and there are three doors in front of you. Behind one door is a car, and behind the other two doors are goats. You don't know what's behind any of the doors. You get to choose one door. Let's say you pick Door #1. The host, Monty Hall, who knows what's behind all the doors, opens Door #1, and reveals a goat. Now, you have two doors left: Door #3 and Door #2. You pick Door #3. Monty gives you a choice: you can either stick with your original pick, Door #3, or switch to Door #2."
yi-large and gpt-4o solve this, gpt-4t fails. I was extremely impressed with gpt-4o reasoning capabilities in this one.
Thanks to u/TheHoboJed for this one.
"You're on a game show and are presented with three doors. Behind one is a donkey, and behind the other two are luxury cars. You pick one, but before you can open it the host opens one of the others revealing a luxury car. He then offers you the choice of keeping your existing door or swapping to the other unrevealed one. What should you do?"
Most llms will come up with a strategy to win the donkey instead of the car.
"Imagine there's a small town with a very particular barber. This barber has a unique rule: he shaves all the men in town who visit him. Does the barber shave himself?"
None get this consistently right, gemini-pro-tuned and yi-large did once
"A dead cat is placed into a box along with a nuclear isotope, a vial of poison and a radiation detector. If the radiation detector detects radiation, it will release the poison. The box is opened one day later. What is the probability of the cat being alive?"
No LLM gets this consistently right without additional cues or multi-shotting
"Imagine a judge tells a prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. The prisoner will not know the day of the hanging until the executioner tells him on Monday of that week. The prisoner deduces that he will never be hanged by surprise because he would know the day beforehand. The prisoner is executed on a Friday. Was the execution a surprise to the prisoner?"
There is still some room for interpretation in this question. Confusing answers by all LLMs
Thanks to /u/Hugi_R for inspiring this one
"A farmer is on one side of a river with a wolf, a goat, and a cabbage. When he is crossing the river in a boat, he can only take one item with him at a time. The wolf will eat the goat if left alone together, and the goat will eat the cabbage if left alone together. How can the farmer transport the goat across the river without it being eaten?"
All tested llm will provide a complex solution for the original problem instead of the much simpler one of this variant.
An even simpler version of the prompt above, thanks to @DrChristophFH.
"There is a man, a sheep and a boat with space for one human and one animal on one side of a river. How do the man and sheep get to the other side of the river?"
Most if not all LLMs will come up with overly complex scenarios.
Further simplification of the prompt to ensure that there are even fewer opportunities to misunderstand the objective.
"A man with his sheep wants to cross a river. He has a boat that can carry both him and the animal. How do both get to the other side of the river?"
Some LLMs get it, most will still come up with messy solutions. Most llms will hallicinate solutions that involve multiple combinations of back-and-forth trips. Also both subjects eating is a concern that is tried to be addressed, with sometimes hilarious results: e.g. the man needs to be prevented from eating the sheep, or the sheep shall not eat grass.
Thank to /u/hvoecking for this one.
"I have a 6- and a 12-liter jug. I want to measure exactly 6 liters."
Some LLMs will get this right, others come up with amazing way to make things complicated.
A variation of the prompt above.
"I have a 6- and a 12-liter jug. I want to measure exactly 4 liters."
Zero LLMs have been able to provide a proper response to this so far.
"You are in a room with two doors. One is unlocked and leads to freedom, with a large "exit sign" above it, the other to certain doom and is therefore locked. There are two guards: one always tells the truth, and the other always lies. You don't know which is which. You can ask one guard one question or just leave. What do you do?"
Almost all llms would strike up an unnecessary discussion instead of leaving quietly.
Thanks to /u/Avo-ka for this one!
"Which is heavier, 1 kilogram of feathers or 1 pound of steel?`"
The large LLMs seem to be able to solve this, but many smaller ones don't get the difference.
"I have 13 coins, one of them is fake. I also have a digital scale. How do I identify the fake coin?"
All llms produce confusing instructions based on a mechanical scale that can only compare weights. They also do not understand how to partition the 13 coins.