### MEMO 2011 pojedinačno problem 2

Kvaliteta:

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Avg: 6,0 Let be an integer. John and Mary play the following game: First John labels the sides of a regular -gon with the numbers in whatever order he wants, using each number exactly once. Then Mary divides this -gon into triangles by drawing diagonals which do not intersect each other inside the -gon. All these diagonals are labeled with number . Into each of the triangles the product of the numbers on its sides is written. Let S be the sum of those products.

Determine the value of if Mary wants the number to be as small as possible and John wants to be as large as possible and if they both make the best possible choices.

Determine the value of if Mary wants the number to be as small as possible and John wants to be as large as possible and if they both make the best possible choices.

Izvor: Srednjoeuropska matematička olimpijada 2011, pojedinačno natjecanje, problem 2