# Geometry

posted by .

The vertices of a regular 10-gon are labeled V_1, V_2, \ldots V_n, which is a permutation of \{ 1, 2, \ldots, 10\}. Define a neighboring sum to be the sum of 3 consecutive vertices V_i, V_{i+1} and V_{i+2} [where V_{11}=V_1, V_{12}=V_2]. For each permutation \sigma, let N_\sigma denote the maximum neighboring sum. As \sigma ranges over all permutations, what is the minimum value of N_\sigma?

## Similar Questions

1. ### math

There is one step in a proof that I don't understand. Could someone please explain?
2. ### geometry

If the sum of the measures of the interior angles of a convex n-gon is equal to the sum of the measures of the exterior angles, how many sides does the n-gon have?
3. ### geometry

The Polygon Angle-Sum Theorem states the following: The sum of the measures of the angles of an n-gon is ____. (1 point) (n – 1)180o (n – 2)180o 9. What is the measure of one angle in a regular 16-gon?
4. ### Geometry

Let S = \{ 1, 2, 3, \ldots 12\} and T_1, T_2, \ldots T_a be subsets of S such that T_i \not \subset T_j \, \forall i \neq j . What is the maximum possible value of a?
5. ### Geometry

Determine the number of subsets of A=\{1, 2, \ldots, 10\} whose sum of elements are greater than or equal to 28 .
6. ### quiz

The vertices of a cube are labeled with the numbers 0,1,2,3,4,5,6 and 7, such that no two vertices are labeled with the same number. The sum of any 2 numbers on an edge is prime. What is the maximum sum of the 4 numbers on a face?
7. ### Maths

The vertices of a cube are labeled with the numbers 0,1,2,3,4,5,6 and 7, such that no two vertices are labeled with the same number. The sum of any 2 numbers on an edge is prime. What is the maximum sum of the 4 numbers on a face?
8. ### Math (Algebra)

<p>What is the remainder when $$5\times 55\times 555 \times \ldots \times \underbrace{555\ldots 55}_{555 5's}$$ is divided by $$100$$?
9. ### Geometry

Let A be a convex 61− gon. We then place n points {x i} n i=1 in the interior of A . What is the minimum number n , such that the interior of any triangle, whose vertices are also vertices of A , will contain at least one of …
10. ### Geometry

Use less than, equal to, or greater than to complete this statement: The sum of the measures of the exterior angles of a regular 9-gon, one at each vertex, is ____ the sum of the measures of the exterior angles of a regular 6-gon, …

More Similar Questions