i need help soon. i know the optimal sum is 36... need answer, ty!

For each arrangement of the ten numbers 1, 4, 7, 10, 13, 16, 19, 22, 25, and 28 around a circle, let N denote the largest of the ten sums obtained by adding three consecutive numbers. What is the smallest value of N that can be obtained?

Guest Jan 16, 2019

#1**+2 **

I have no idea how to do this but I would be interested if anyone else has an approach.

Melody Jan 17, 2019

#2**+3 **

I've done a few Monte-Carlo simulations of this and get 48 as the smallest value for N. Here are a few arrangements that give this (remember that the numbers are arranged in a circle, rather than the straight line shown here):

__16 22 10__ __7 28 13__ 1 __19 25 4__

__7__ __10 25 13__ __4 28 16__ 1 __19 22__

__4__ __16 10 22__ __7 13 28__ 1 __19 25__

Alan Jan 17, 2019