whatever model the website currently feels like using
You cannot simply handwave this away. "ChatGPT" models range from GPT 5.5 on "Light" effort to GPT 6 Astra with "Ultra" effort.
The latter yields as good an answer as you could expect for a question that is still poorly formed ("close enough," WTF does that mean?): https://chatgpt.com/share/6aab1e43-da3c-83e8-9ec4-1b63cec2c1...
When I click your share, it shows the model. When I click into my chat, it just says "High". I did ask the model what it was and it said "GPT-5.6 Sol".
Oh, and I don't even have a "light" option, and I'm signed in to a Pro account.
(I continue to despise the chatgpt.com frontend.)
In any case, I tried again forcing GPT-6 Astra Pro (apparently I can't choose GPT-6 Astra non-Pro) and gave the same prompt. It searches the web and gives a long-winded answer, including:
> 7. Does unspecified sphere–sphere friction change the static answer?
> For ordinary ideal point contacts in this regular-tetrahedral configuration, it does not. Gravity, the floor reactions, and the frictionless equatorial rope exert no torque about any sphere’s center. The tangential intersphere forces must therefore balance their torques by themselves.
I'm glad it contemplated the possibility of friction, but it forgot about the table/floor there. So maybe this is a little better than Sol?
Yeah, it's strange that people who should be knowledgeable in experimentation ignore that. "I heard that people enjoy skiing. I've tried skiing on whatever surface happened to be on a nearby hill and it didn't work!"