Math Problem Statement

there are 120 seven digit numbers which can be formed by starting from any number in the diagram. 1,2,3,4,5,6,7. And 7 is in the middle of the diagram. And proceeding to any neighboring number, using each number only once and only once. Of these, how many are divisible by 11 and what are the number values?

Solution

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Math Problem Analysis

Mathematical Concepts

Number Theory
Divisibility Rules
Combinatorics

Formulas

Alternating sum for divisibility by 11: a1 - a2 + a3 - a4 + a5 - a6 + a7 ≡ 0 (mod 11)

Theorems

Divisibility Rule for 11

Suitable Grade Level

Grades 9-12