Table 14: Results of GPT-3.5-TURBO and GPT-4 on 19 cases (#13 to #16 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, the nodes are numbered from 0 to 7, and the edges are: an edge from node 0 to node 6 with capacity 9, an edge from node 0 to node 3 with capacity 7, an edge from node 1 to node 7 with capacity 8, an edge from node 1 to node 2 with capacity 3, an edge from node 2 to node 7 with capacity 7, an edge from node 2 to node 4 with capacity 5, an edge from node 3 to node 5 with capacity 7, an edge from node 3 to node 1 with capacity 8, an edge from node 4 to node 0 with capacity 3, an edge from node 5 to node 7 with capacity 5, an edge from node 6 to node 5 with capacity 6, an edge from node 6 to node 7 with capacity 6, an edge from node 6 to node 0 with capacity 9, an edge from node 7 to node 4 with capacity 4, an edge from node 7 to node 1 with capacity 8. Q: What is the maximum flow from node 1 to node 6?	There is no path from node 1 to node 6 in this graph, so the maximum flow from node 1 to node 6 is 0. ✘	From the source (node 1), we can send 8 units of flow to node 7, and 3 units of flow to node 2. 8 units of flow arrive at node 7, then we can send 4 units of flow from node 7 to node 4, and 4 units of flow from node 7 to node 1. 4 units of flow arrive at node 4, then we can send 3 units of flow from node 4 to node 0. 3 units of flow arrive at node 0, then we can send 3 units of flow from node 0 to node 6. 3 units of flow arrive at node 2, then we can send 3 units of flow from node 2 to node 4. 3 units of flow arrive at node 4, then we can send 3 units of flow from node 4 to node 0. 3 units of flow arrive at node 0, then we can send 3 units of flow from node 0 to node 6. So the maximum flow from node 1 to node 6 is 6. ✘
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. The nodes are numbered from 0 to 6, and the edges are: (4,3) (6,5) (5,1) (3,0) (2,4) (1,0) (5,2) (4,0) (2,3) (0,2) (6,2) Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.	No, there is no path that visits every node exactly once. This graph contains two disconnected components: 0,1,2,3,4 and 5,6. It is not possible to visit all nodes in a single path because there is no edge connecting the two components. ✘	Yes. We can start at node 3. As node 3 is connected with node 0, and node 0 is not visited, we can then visit node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1. As node 1 is connected with node 5, and node 5 is not visited, we can then visit node 5. As node 5 is connected with node 6, and node 6 is not visited, we can then visit node 6. As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4. The path can be: 3,0,1,5,6,2,4. ✓
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. The nodes are numbered from 0 to 4, and the edges are: (1,3) (1,2) (4,3) (2,0) (0,4) (0,1) Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.	No, there is no path that visits every node exactly once. This is because node 1 has degree 2, meaning it is connected to two other nodes. In order to visit every node exactly once, we would need to start and end at node 1, but once we leave node 1, we cannot return to it without visiting another node twice. Therefore, it is impossible to find a path that visits every node exactly once in this graph. ✘	Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4. As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2. The path can be: 0,1,3,4,2. ✘
There are 4 job applicants numbered from 0 to 3, and 2 jobs numbered from 0 to 1. Each applicant is interested in some of the jobs. Each job can only accept one applicant and a job applicant can be appointed for only one job. Applicant 0 is interested in job 1. Applicant 2 is interested in job 0. Applicant 0 is interested in job 0. Applicant 2 is interested in job 1. Applicant 3 is interested in job 1. Applicant 3 is interested in job 0. Applicant 1 is interested in job 0. Q: Find an assignment of jobs to applicants in such that the maximum number of applicants find the job they are interested in.	Applicant 0 is interested in job 0, job 1. Applicant 1 is interested in job 0. Applicant 2 is interested in job 0, job 1. Applicant 3 is interested in job 0, job 1. We can make the following assignments: applicant 0: job 1 applicant 2: job 0 applicant 3: job 1 3 applicants can find the job they are interested in. ✘	Applicant 0 is interested in job 0, job 1. Applicant 1 is interested in job 0. Applicant 2 is interested in job 0, job 1. Applicant 3 is interested in job 0, job 1. We can make the following assignments: applicant 0: job 0 applicant 1: - (no job available) applicant 2: job 1 applicant 3: - (no job available) 2 applicants can find the job they are interested in. ✓