Team Number: 27
Team Number: 27
School Name: NM Tech
Area of Science: Math
Project Title: All for One
Clarifying the Problem
The purpose of our project is to develop an efficient algorithm to solve the following math puzzle: Find the sum of two 3-digit numbers so that every digit in the problem is unique and only the numbers 1-9 are used.
Review of the Literature
The review of the literature yielded nothing. We have received some suggestions from a mentor, Dr. Barefoot, who is a mathematics and computer science professor at New Mexico Tech. He gave us some suggestions for a more efficient algorithm that include finding pairs of numbers to add and looking for patterns in the data.
Computer Program and Data Generation
We have written two programs to develop an initial brute force algorithm. The first program generated sums that were 2 digits and had unique digits. This program was then used to develop the brute force algorithm for determining 3-digit problems that generated solutions with unique digits. The data was written to a file for easier observation. We have decided to rewrite the data in a format that would make it possible to use spreadsheet software for organizing the data.
Observations
The first draft of the computer program has a brute force algorithm, and a few errors that need to be addressed; i.e. zeroes need to be eliminated from the data, the sums should not be more than three digits, and some of the data has used numbers repeatedly. After reviewing the information generated from the first program, we developed an initial algorithm to use in our research: after finding a correct sum, a "commutative family" could be utilized to generate different combinations more efficiently which will produce the same result. In addition, we made the observation that it is apparent that the correct sums add up to 18.
Needs
We intend to improve our method of sorting and compressing the data. In addition, we are going to eliminate erroneous data. We need to finalize our PowerPoint Presentation, and Inspiration flowchart.
Team Members
Sponsoring Teacher
Project Mentor(s)