> and it just spit out the correct answer instantly.
What did it spit out? Because there is more than one solution (or none, if unhelpfully pedantic).
It's certainly possible with practice to quickly mentally figure out that 3.75 * 4 is the least whole multiple, so n = 4.
Quick and dirty 2,2 makes a possible median and so 1, 2, 2, 10 and 2,2,2,9 are clearly solutions, since x+y= 15-4 where 0<x≤2, y>2 is not hard to do mentally. I struggle to call this a hard or enormous mental calculation. (Not missing the other solution, just acknowledging it takes an extra step - apparently it is hard for ChatGPT!)
I'm not terribly impressed by that last one especially for nearly 2 minutes of "thinking". I also don't love that it keeps saying, set, set... A helpful tutor should at least gently point out these are not strictly sets. There's no solution of a set of positive integers that solves that problem.
If your GPT didn't give those 3 solutions right off the bat (I could not get mine to) and clarify they are not formally sets, it is a type of failure. Sure you can argue that a better prompt would improve it, but this is a problem, non experts putting in ill-formed or flawed prompts and not getting useful feedback where an expert human would be more helpful. A good human will tell you it's a multiset and in general there isn't a unique solution so the problem could be phrased better.
I asked o1-preview to make the question more rigorous and it came up with "Find all sets...".
What did it spit out? Because there is more than one solution (or none, if unhelpfully pedantic).
It's certainly possible with practice to quickly mentally figure out that 3.75 * 4 is the least whole multiple, so n = 4. Quick and dirty 2,2 makes a possible median and so 1, 2, 2, 10 and 2,2,2,9 are clearly solutions, since x+y= 15-4 where 0<x≤2, y>2 is not hard to do mentally. I struggle to call this a hard or enormous mental calculation. (Not missing the other solution, just acknowledging it takes an extra step - apparently it is hard for ChatGPT!)
4o actually struggled with keeping a median straight: https://chatgpt.com/share/67225a67-48ec-800f-a581-9651e7f65d...
And o1-preview had a very difficult time coming up with all solutions. https://chatgpt.com/share/67225ead-c9bc-800f-bcc1-067aacbf2b...
I'm not terribly impressed by that last one especially for nearly 2 minutes of "thinking". I also don't love that it keeps saying, set, set... A helpful tutor should at least gently point out these are not strictly sets. There's no solution of a set of positive integers that solves that problem.
If your GPT didn't give those 3 solutions right off the bat (I could not get mine to) and clarify they are not formally sets, it is a type of failure. Sure you can argue that a better prompt would improve it, but this is a problem, non experts putting in ill-formed or flawed prompts and not getting useful feedback where an expert human would be more helpful. A good human will tell you it's a multiset and in general there isn't a unique solution so the problem could be phrased better.
I asked o1-preview to make the question more rigorous and it came up with "Find all sets...".