You can also put the AI in the first person's shoes. Prompt: You are standing in a circle, there are 2 other people in the circle with you, everyone in the circle, has a positive integer above their head, no one knows what the number above their own head is but can see the numbers above the heads of the other people. You see that the person infront of you on the left has 26 above their head. The person on the right has 39 above their head. You are told that the sum of two of the numbers is the third number. You are asked what the number above your head is, the option is the sum, 65, or 13, as 26 + 13 = 39. You don't know which one it is, and you say so. The second person is asked the number above their head. They also say they dont know, the third person also says they dont know. What is your number?

Gemini 2.5 and claude 3.7 thinking get it right, o3 mini and 4o get it wrong