Table 12: Results of GPT-3.5-TURBO and GPT-4 on 19 cases (#7 to #9 example) through the eight tasks. We omitted the COt in-context exemplars in the table.
Question	GPT-3.5-TURBO	GPT-4
In an undirected graph, the nodes are numbered from 0 to 6, and the edges are: An edge between node 0 and node 2 with weight 1, An edge between node 3 and node 0 with weight 4, An edge between node 5 and node 0 with weight 2, An edge between node 4 and node 0 with weight 3, An edge between node 0 and node 1 with weight 4, An edge between node 0 and node 6 with weight 2, An edge between node 2 and node 1 with weight 2, An edge between node 3 and node 1 with weight 3, An edge between node 4 and node 1 with weight 3, An edge between node 1 and node 6 with weight 2, An edge between node 2 and node 5 with weight 4, An edge between node 2 and node 4 with weight 3, An edge between node 6 and node 2 with weight 2, An edge between node 3 and node 5 with weight 4, An edge between node 4 and node 3 with weight 2, An edge between node 3 and node 6 with weight 4, An edge between node 4 and node 5 with weight 3, An edge between node 4 and node 6 with weight 1, An edge between node 6 and node 5 with weight 2. Q: Give the shortest path from node 2 to node 3.	All the paths from node 2 to node 3 are: 2,0,3 with a total weight of 1 + 4 = 5, 2,1,3 with a total weight of 2 + 3 = 5, 2,4,3 with a total weight of 3 + 2 = 5. The weight of path 2,0,3 is the smallest, so the shortest path from node 2 to node 3 is 2,0,3 with a total weight of 5. X	All the paths from node 2 to node 3 are: 2,0,3 with a total weight of 1 + 4 = 5, 2,1,3 with a total weight of 2 + 3 = 5, 2,1,0,3 with a total weight of 2 + 4 + 4 = 10, 2,1,6,3 with a total weight of 3 + 2 = 5, 2,4,0,3 with a total weight of 3 + 3 + 4 = 10, 2,4,1,3 with a total weight of 3 + 3 + 3 = 9, 2,4,1,0,3 with a total weight of 3 + 3 + 4 = 14, 2,4,1,6,3 with a total weight of 3 + 3 + 4 = 12, 2,5,0,3 with a total weight of 4 + 2 + 4 = 10, 2,5,4,3 with a total weight of 4 + 2 + 4 = 16, 2,5,4,1,3 with a total weight of 4 + 5 + 3 + 4 = 16, 2,5,4,1,3 with a total weight of 4 + 5 + 3 + 3 = 15, 2,5,6,3 with a total weight of 4 + 6 + 4 = 14, 2,6,1,3 with a total weight of 2 + 2 + 3 = 7, 2,6,1,0,3 with a total weight of 2 + 2 + 4 + 4 = 12, 2,6,5,0,3 with a total weight of 2 + 5 + 5 + 2 = 14. The weight of paths 2,0,3, 2,1,3, and 2,4,3 is the smallest. So, there are three shortest paths from node 2 to node 3, which are 2,0,3; 2,1,3; and 2,4,3, each with a total weight of 5. X
In a directed graph with 5 nodes numbered from 0 to 4: node 2 should be visited before node 4 node 2 should be visited before node 1 node 2 should be visited before node 0 node 4 should be visited before node 1 node 4 should be visited before node 0 Q: Can all the nodes be visited? Give the solution.	This is not possible as there is a cycle between nodes 0, 1, and 4. Node 2 cannot be visited before nodes 0, 1, and 4, and nodes 0, 1, and 4 cannot be visited before node 2. Therefore, it is not possible to visit all the nodes in this graph. X	Since no nodes are required to be visited before node 2 and node 3, node 2 and node 3 can be visited first. Since visiting node 4 requires visiting node 2 first, after node 2 is visited, node 4 can be visited. Since visiting node 0 requires visiting node 2, node 4 first, after node 2 and node 4 are visited, node 0 can be visited. Since visiting node 1 requires visiting node 2, node 4 first, after node 2 and node 4 are visited, node 1 can be visited. So the solution is: 2,3,4,0,1. X
In a directed graph with 5 nodes numbered from 0 to 4: node 0 should be visited before node 1 node 1 should be visited before node 2 node 3 should be visited before node 1 node 3 should be visited before node 2 node 4 should be visited before node 3 node 4 should be visited before node 0 node 4 should be visited before node 1 Q: Can all the nodes be visited? Give the solution.	This graph has a cycle, which means it is not possible to visit all nodes in a valid order. Specifically, there is a cycle between nodes 1, 2, and 3, which cannot be resolved based on the given constraints. X	Since no nodes are required to be visited before node 4, node 4 can be visited first. Since visiting node 0 and node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited. Since visiting node 1 requires visiting node 0 and node 3 first, after node 0 and node 3 are visited, node 1 can be visited. Since visiting node 2 requires visiting node 1 and node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2. X