Question 89
Morgane and Bosphore play the following game. Morgane writes the integers $1$ through $8$ at the vertices of a regular octagon, one integer at each vertex. Bosphore then chooses a vertex and calculates the sum of the numbers at that vertex and its two neighbors. Calling this sum $s$, he gives Morgane $s$ candies.
Bosphore chooses a vertex so as to give Morgane as few candies as possible, while Morgane arranges the integers $1$ through $8$ so as to receive as many candies as possible. Prove that Bosphore will give her $12$ candies.
Bosphore chooses a vertex so as to give Morgane as few candies as possible, while Morgane arranges the integers $1$ through $8$ so as to receive as many candies as possible. Prove that Bosphore will give her $12$ candies.