Table 13: Results of GPT-3.5-TURBO and GPT-4 on 19 cases (#10 to #12 example) through the eight tasks. We omitted the COt in-context exemplars in the table.
Question	GPT-3.5-TURBO	GPT-4
In a directed graph with 6 nodes numbered from 0 to 5: node 0 should be visited before node 5	Since no nodes are required to be vis- ited before node 3 and node 4, node 3 and node 4 can be visited first. Since visiting node 0 requires visiting node 3 first, after node 3 is visited, node 0 can be visited. Since visiting node 1 requires visiting node 0, node 2, node 3 first, after node 0, node 2, and node 3 are visited, node 1 can be visited. Since visiting node 5 requires visit- ing node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. Since visiting node 2 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 2 can be visited. So the solution is: 3,4,0,2,1,5.	Since no nodes are required to be vis- ited before node 3 and node 4, node 3 and node 4 can be visited first. Since visiting node 0 requires visiting node 3 and node 4 first, after node 3 and node 4 are visited, node 0 can be vis- ited. Since visiting node 5 requires visiting node 0 and node 3 first, after node 0 and node 3 are visited, node 5 can be visited. Since visiting node 1 requires visiting node 0, node 2, and node 3 first, node 2 must be visited before node 1. Since visiting node 2 requires visiting node 4 and node 5 first, after node 4 and node 5 are visited, node 2 can be visited. Now, since node 0, node 2, and node 3 have been visited, node 1 can be vis- ited. So the solution is: 3,4,0,5,2,1.
In a directed graph, the nodes are numbered from 0 to 5, and the edges are: an edge from node 1 to node 3 with capacity 4, an edge from node 1 to node 0 with capacity 9, an edge from node 2 to node 1 with capacity 4, an edge from node 3 to node 1 with capacity 4, an edge from node 4 to node 3 with capacity 1, an edge from node 4 to node 5 with capacity 2, an edge from node 5 to node 1 with capacity 4, an edge from node 5 to node 0 with capacity 7. Q: What is the maximum flow from node 4 to node 0?	There is no path from node 4 to node 0, so the maximum flow from node 4 to node 0 is 0.	From the source (node 4), we can send 1 unit of flow to node 3, and 2 units of flow to node 5. 1 unit of flow arrives at node 3, then we can send 1 unit of flow from node 3 to node 1. 2 units of flow arrive at node 5, then we can send 2 units of flow from node 5 to node 0. 1 unit of flow arrives at node 1, then we can send 1 unit of flow from node 1 to node 0. The total unit of flow arrives at node 0 is 3. So the maximum flow from node 4 to node 0 is 3.
In a directed graph, the nodes are numbered from 0 to 7, and the edges are: an edge from node 0 to node 6 with capacity 1, an edge from node 0 to node 7 with capacity 10, an edge from node 2 to node 1 with capacity 9, an edge from node 2 to node 7 with capacity 8, an edge from node 3 to node 1 with capacity 9, an edge from node 3 to node 6 with capacity 10, an edge from node 3 to node 4 with capacity 7, an edge from node 4 to node 6 with capacity 1, an edge from node 5 to node 3 with capacity 7, an edge from node 5 to node 2 with capacity 9, an edge from node 6 to node 4 with capacity 1, an edge from node 7 to node 5 with capacity 8, an edge from node 7 to node 6 with capacity 5. Q: What is the maximum flow from node 2 to node 4?	From the source (node 2), we can send 8 units of flow to node 7, and 9 units of flow to node 1. 8 units of flow arrive at node 7, then we can send 5 units of flow from node 7 to node 6, and 3 units of flow from node 7 to node 5. 9 units of flow arrive at node 1, then we can send 9 units of flow from node 3 to node 1. 9 units of flow arrive at node 6, then we can send 1 unit of flow from node 6 to node 4. 7 units of flow arrive at node 3, then we can send 7 units of flow from node 3 to node 4. The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 4 is 8.	From the source (node 2), we can send 9 units of flow to node 1, and 8 units of flow to node 7. 9 units of flow arrive at node 1, then we can send 9 units of flow from node 1 to node 3. 8 units of flow arrive at node 7, then we can send 8 units of flow from node 7 to node 5, and 5 units of flow from node 7 to node 6. 8 units of flow arrive at node 5, then we can send 7 units of flow from node 5 to node 3, and 1 unit of flow from node 5 to node 2. 14 units of flow arrive at node 3, then we can send 14 units of flow from node 3 to node 4. The total unit of flow arrives at node 4 is 14. So the maximum flow from node 2 to node 4 is 14.