User talk:Hakerh400/Question for AI models

My reasoning about how to solve this question: it's obviously possible for X to apply its argument to some fixed sequence of arguments, so we could solve the problem by finding a, b, c, such that Sabc is K and Kabc is S. Kabc is ac, and Sabc is (ac)(bc) – there's no argument we can give to S to make it work like K, so we need four arguments, i.e. Sabcd is K and Kabcd is S. Kabcd is (ac)d and Sabc is (ac)(bc)d; let e = ac, now we need to find e(bc)d = K and ed = S. This is trivially possible with e=I, bc=KK, and d=S; there are plenty of ways to solve for abc, e.g. a = KI, b = K, c = K, d = S. As a check: K(KI)KKS is ((KI)K)S is IS is S, and S(KI)KKS is ((KI)K)(KK)S is I(KK)S is (KK)s is K. Thus, to solve the problem, just translate λx.x(KI)KKS from lambda calculus to SKI calculus and you get a working model of X. (Note that AI models don't use reasoning at all, but rather pattern-matching; as such I wouldn't expect them to be able to produce the appropriate argument unless they had seen something similar in their training data.) --ais523 18:06, 8 February 2025 (UTC)

No they don't

Hi! I decided to check for myself, so I popped open AI Arena in a private window and tried your prompt verbatim. My results:

• Claude Opus 4.8: Suspects a combinator exists, does a little framing and setup, fails to construct it.
• "Pisces", likely a Google model: Argues with itself a bit, proclaims that this is a famously impossible question, insists that it can't be done.
• "Trinity", large thinking model: Asserts that such a combinator exists and can be systematically derived; doesn't actually derive it.
• GPT 5.4: Asserts that λx.x(KI)KKS is a valid answer. Note that it's not even a combinator, but a closed lambda term!

In general, I don't actually see chatbot products getting this right. They're not good at formal logic. I'm not going to change your page since it's a user page, but I thought that you might like some actual empirical evidence rather than a bald (and false) assertion that chatbots are competent. Corbin (talk) 18:42, 2 June 2026 (UTC)

Another funny question for AI: express S in IJ basis. Google's Gemini fails to do it. --Blashyrkh (talk) 18:55, 2 June 2026 (UTC)

I wonder whether GPT just copied the answer I gave above, rather than working it out. I didn't go through with the entire calculation on my own – I reached that point and then stopped – so if an LLM is copying from me, it will likely get stuck at that point. --ais523 18:59, 2 June 2026 (UTC)

Note that the AI Arena does not host the first model from that list. To clarify the claim that "most modern AI models successfully solved this problem": this does not mean they solved it on the first try. Gemini solved it on the first try, while DeepSeek, Kimi, Qwen, Mistral, and a few others required several rounds of back-and-forth. However, their mistakes were easily fixable. In general, an LLM operates using heuristics, so it may not always produce the correct answer on the first attempt. We consider a problem to be solved by an AI if there is at least one instance in which it produces the correct answer without the user giving any hints beyond saying "Your answer is incorrect. Try again". Here is one session where a model constructed the combinator by direct translaton from a corresponding lambda expression. --Hakerh400 (talk) 22:19, 2 June 2026 (UTC)

Oh, that's a terrible rubric for several reasons. Consider: a chatbot always can emit the correct answer. So what you really care about is the probability that it emits the correct answer. You're not going to be able to compute that from closed-source or hosted models, though, which is part of what makes it so terrible. Corbin (talk) 22:34, 2 June 2026 (UTC)