- #1

JimBob81345

## Homework Statement

My teacher gave our class this problem to do Two players take turns placing an unused number from {1; 2; 3; 4; 5; 6; 7; 8} into one of the empty squares in a 2 by 4 array. The game ends once all the squares are tiled. The 1st player wins if the product of the numbers in the top row is greater. The second player wins if the product of the numbers in the bottom row is greater. What is the perfect strategy for each player? Please help me, if you cannot provide the answer please give me a hint. This problem has been bugging me for so long.

Reference https://www.physicsforums.com/threads/help-with-some-problems.927068/

## Homework Equations

## The Attempt at a Solution

I am stuck, because the perfect strategy depends on the other person's play. And there are 8! ways this game can be played out.

I know the first player should put 1 on the second row.