{"type":"ScholarlyArticle","title":"A Number Theory Approach to Problem Representation and Solution","authors":[{"name":"Stewart N. T. Shen","slug":"stewart-n-t-shen","given":"Stewart N. T.","family":"Shen","affiliation":""},{"name":"Edward R. Jones","slug":"edward-r-jones","given":"Edward R.","family":"Jones","affiliation":""}],"abstract":"A number theory approach to problem solving is presented using the tower of cubes puzzle as an example. Some conventional methods of solving the puzzle are first discussed. The puzzle is then thoroughly studied using an entirely different approach. Special numbers are used to represent the different colors on the sides of the cubes. A description matrix is used to compress the problem representation. The solution method becomes very efficient because of the concise representation of the problem. Two theorems are developed to verify the solution method. A generalization of the puzzle is also discussed.","doi":null,"url":"https://ijcai.org/proceedings/1973/75","pdf":"https://ijcai.org/proceedings/1973/0075.pdf","markdown":"https://ijcai.org/proceedings/1973/75.md","bibtex":"https://ijcai.org/proceedings/1973/bibtex/75","volume":{"slug":"1973","title":"Proceedings of the Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1973","url":"https://ijcai.org/proceedings/1973/","year":1973,"location":"Stanford, California, USA","dates":"20-23 August 1973","editors":"Nils J. Nilsson","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"General Problem Solving","track":"General Problem Solving","number":75,"pages":{"first":606,"last":610},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}