Can LLMs identify 16 cards in 45 bit-queries?

Re:Can LLMs identify 16 cards in 45 bit-queries? by napping_penguin on Tuesday July 28, 2026 @02:39PM (#49088112)

You are right, your argument establishes the lower bound: D(4) >= 5 (you will need at least 5 questions in the worst case).

The interesting bit is to come up with a strategy to make 5 adaptive queries that will guarantee you know all the 4 cards no matter what the response you got to the queries.

As a simple example: Suppose I do the following (static) set of 5 questions:

- Is the first card Red?

- Is the first card King?

- Is the second card Red?

- Is the second card King?

- Is the third card Red?

You can see that there might be a situation where these 5 questions are not enough to uniquely determine the arrangement (for instance, in case you got answers Yes, Yes, Yes, No, No respectively).

More succinctly, 5 is the information theoretic lower bound but that does not mean it is achievable and that is precisely what the post is about. Is the information theoretic lower bound achievable?

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Re:Can LLMs identify 16 cards in 45 bit-queries? by mcphage on Tuesday July 28, 2026 @06:38PM (#49090929)

…then why does the page keep saying it’s always possible in less than 5 questions, if it sometimes requires 5 questions?

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Re:Can LLMs identify 16 cards in 45 bit-queries? by napping_penguin on Tuesday July 28, 2026 @08:41PM (#49091968)

Ah, sloppy language on my part. It should be 5 of fewer questions. I'll fix it, thank you!

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