ChatGPT problem statement - graph, spatial modeling

[rahul101001000]

Consider the following problem - given a 3x3 chessboard with 2 white knights on the top corners and 2 black knights on the bottom corners, can we move the white knights to the bottom corners and the black knights to the top corners without an illegal move. How many moves will this take? (A standard problem from Russian Math Circles)

Now ChatGPT gets the answer right and seems to have a good model for how to solve it - brute force through all states.

Now a smarter way of solving this is to toss all squares on a graph with legal moves defining the edges. It turns out this is a nice circle with the middle square a lone node at the center. A high schooler (maybe even middle schooler can quickly see that the knights cannot cross each other without two of them getting on the same square. 

ChatGPT doesn't get the graph way right even after asking it to do so. This is because it has been trained with the state machine brute force model for chess but not a graph model.

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Can we figure out a LLM or maybe LKM Large Knowledge Model that can be trained with graphs, spatial reasoning, math models et al?