I asked three different Artificial Intelligences an arithmetical riddle and got three different answers, which each claimed was the only possibility. Here is the riddle:
Alice and Bill each secretly pick an integer from 1 to 30.
Alice: Is your number double mine?
Bill: I don’t know. Is your number double mine?
Alice: I don’t know. Is your number less than mine?
Bill. I’m not going to answer that. I know your number!
- What is Alice’s number and how does Bill know it?
And here are their answers:
- ChatGPT: 18
- Claude: 8
- Perplexity: 4
Your thoughts?
Dear Karl Pfeifer,
I'd like to add to the conclusion of your riddle. According to DeepSeek, it's 14. Proceeding on 4 cases with probabilities, the final answer is Alice's number is 14. Bill deduces this by realizing that his number must be less than Alice's, and the only even number in the possible range where this holds is 14.
In cases where nothing is known, it seemed more accurate to me to go through the cases. Thank you.
Best Regards,
Dr Kubilay Ayturan
Kubilay Ayturan
Interesting. 14 is actually the answer I got on my own, but I wasn't very confident about it, since my reasoning wasn't completely systematic. I also thought there might be an ambiguity in that it didn't seem to be precluded that Alice and Bill could've picked the same number.
Here's is Perplexity's detailed answer:
https://www.perplexity.ai/search/solve-this-riddle-096xIiVaSMySJ.5CeUdNrQ
Karl Pfeifer
This time I tried the riddle with deepthink(R1), one of the deepseek features. The result was given after about 14 minutes. You will be surprised at the result. I am sharing the link.
Here's is Deepseek's detailed answer:
https://chat.deepseek.com/a/chat/s/9ad6f764-4e7c-4104-8ca1-7b3bfca6d25d
Kubilay Ayturan
The link doesn't take me to the answer but merely to the start-a-chat page. Can you create a pdf and add it to your answer here?
Kubilay Ayturan
I reentered the riddle on deepseek. It gave a long explanation of why 4 was the answer, with a summary of the 3 main logical steps at the end. I indicated there was a false presupposition in step 1 of the summary, because at that point Bill couldn't know whether his and Alice's numbers were different or the same. After a couple of iterations, Deepseek finally agreed, but then claimed step 2 ruled sameness out. That's as far as I got.
Karl Pfeifer
I'm enclosing the pdf file. It gave the result as 16.
The results of the riddle in Deepseek are respectively 14 - 16 - 4 In fact, even this result shows us that AI has a long way to go. Because in the light of all the results, there is a violation of the principle that science should be repeatable in every environment and give the same result.
Kubilay Ayturan
Yikes, 34 pages!
Achille Varzi showed early on that ChatGPT didn't learn from its mistakes.
Here is a discussion of the riddle I just found on Stack Exchange:
https://math.stackexchange.com/questions/4807985/two-logicians-who-each-pick-a-number-secretly-between-1-and-30
I wonder whether the puzzle might be ill-formed.
Alice: Is your number double mine?
Bill: I don’t know.
In case of odd number he'd know the answer -> Bill has even number
By asking she implies that it may be possible to have double her number -> Alice number must be in range from 1-15
Bill: Is your number double mine?
Alice: I don’t know.
Bill must have less than 7, as above that he couldn't ask whether someone has double his number
In case of not knowing -> Alice number must be multiplication of 4.
Bill options: 2,4,6
Alice options: 4,8,12
Alice: Is your number less than mine?
Bill. I’m not going to answer that. I know your number!
Alice couldn't ask this question in case of having 8 or 12, as she already knows the answer. Therefore, as she asks she has 4.
Karl Pfeifer Kubilay Ayturan Do you think AI would spare me for being able to solve such riddle? :D
Marcin Piotr Walkowiak
I think ChatGPT, Claude and Deepseek will not forgive you :)
But he'll love you for coming to the same conclusion as Perplexity :D