What is the most effective way to make ChatGPT to resolve math problems

Question

What is the most effective prompt to make ChatGPT to be able to resolve this math quiz:

At the Eatery with Multiple Configurations, there are round tables, around which chairs are placed. When a tab has n chairs around it for some integer n>=3, the chairs are labelled 1, 2, 3, ..., n -1, n in order around the table. A table is considered full if no more people can be seated without have two people sit in neighboring chairs. For example, when n = 6, full tables occur when people are seated in chairs labelled {1, 4} or {2, 5} or {3, 6} or {1, 3, 5} or {2, 4, 6}. Thus there are 5 different full tables when n = 6.

Determine all ways in which people can be seated around a table with 8 chairs so that the table is full, in each case giving the labels on the chairs in which people are sitting.

I am using GPT-4 model

I started with this:

Please resolve the problem step by step. Starting with the chair #1, consider each step with gap 1 chair and gap 2 chairs.

It finds out the following:

• Chairs {1, 3, 5, 7}
• Chairs {1, 4, 7}
• Chairs {2, 4, 6, 8}
• Chairs {2, 5, 8}
• Chairs {3, 6} which is wrong.

I then added:

The last one is wrong, chair #1 still sit one more person, it is not full. And your approach is wrong too. you need to consider each jump can be 1 chair or 2 chairs. Therefore you missed combination like {1, 4, 6}. Please redo it.

It still cannot resolve the issue.