You'd have better results if you had prompted it with the actual answer and asked how the first person came to the conclusion. Giving a number in the training set is very easy.
i.e. You observe three people in a magical room. The first person is standing underneath a 65, the second person is standing underneath a 26 and the third person is standing underneath a 39. They can see the others numbers but not the one they are directly under. You tell them one of the three numbers is the sum of the other two and all numbers are positive integers. You ask the first person for their number, they respond that they don't know. You ask the second person for their number, they respond that they don't know. You ask the third person, they respond that they don't know. You ask the first person again and they respond with the correct value, how did they know?
i.e. You observe three people in a magical room. The first person is standing underneath a 65, the second person is standing underneath a 26 and the third person is standing underneath a 39. They can see the others numbers but not the one they are directly under. You tell them one of the three numbers is the sum of the other two and all numbers are positive integers. You ask the first person for their number, they respond that they don't know. You ask the second person for their number, they respond that they don't know. You ask the third person, they respond that they don't know. You ask the first person again and they respond with the correct value, how did they know?
And of course, if it responds with a verbatim answer in the line of https://www.reddit.com/r/math/comments/32m611/logic_question..., we can be pretty confident what's happening under the hood.