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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?

 Jan 16, 2019
 #1
avatar+109468 
+2

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

 Jan 17, 2019
 #2
avatar+29877 
+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

 Jan 17, 2019
edited by Alan  Jan 17, 2019
 #3
avatar+109468 
+1

Thanks Alan :)

Melody  Jan 18, 2019

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