Math Problem Statement
The faces of a standard die are numbered 1, 2, 3, 4, 5, and 6 such that the sum of the numbers on any two opposite faces is 7. Tia writes one number on each vertex of the die such that the number on each face of the die is the greatest common divisor of the numbers at the four vertices of that face. What is the smallest possible sum of the eight numbers Tia writes?
Solution
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Math Problem Analysis
Mathematical Concepts
Number Theory
Greatest Common Divisor (GCD)
Prime Factorization
Formulas
GCD of multiple numbers
Prime factorization of integers
Theorems
Properties of GCD
Prime Factorization
Suitable Grade Level
Grades 10-12
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