# Perfect Stategy -- Placing picked numbers on two rows of a game

• JimBob81345
In summary, the conversation discusses a problem given by a teacher that involves two players taking turns placing numbers in a 2 by 4 array. The game ends when all squares are filled and the first player wins if the product of the numbers in the top row is greater, while the second player wins if the product of the bottom row is greater. The perfect strategy for each player is discussed, with the realization that the game tree is smaller than that of tic-tac-toe and can be easily solved by considering only two possible moves for each player. The goal is not to win, but to force the opponent to lose.
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.

## 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.

JimBob81345 said:

## 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.

## 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.
Welcome to the PF.

Of course we cannot give you the answer -- that is against the PF rules. If I understand the problem statement, the strategy seems straight-forward. The players each have one of the two empty rows assigned to them at the start of the game, right?

Tell us your thinking so far, so we can guide you a bit...

JimBob81345 said:

## 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.

## 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.

How do you know that player 1 should put "1" in row 2? Might it not be better for player 1 to put "8" in row 1?

Last edited:
I have found the Solution.
I realized something very important while solving the problem
Thanks anyways

Sorry, never mind I still need help

The game tree you need to analyse is actually smaller than that of tic-tac-toe. easily done by hand with the following:
- each player has only two possible moves to consider on each move.
- You can see really early if the game is already won. Work out what the product is you need to get to win and see if each player can still get it by using the maximum of the numbers that are left.

JimBob81345 said:
Sorry, never mind I still need help
It's not about winning, it's about forcing your opponent to lose. There is a simple strategy that guarantees that the opponent of the player who goes first loses. Can you find it?

## 1. What is the purpose of placing picked numbers on two rows of a game?

The purpose of placing picked numbers on two rows of a game is to create a strategic layout that maximizes your chances of winning the game. By distributing the numbers across two rows, you can increase your chances of achieving a winning combination.

## 2. How do you determine which numbers to place on the two rows?

The numbers that are placed on the two rows should be carefully selected based on probability and pattern analysis. This involves studying the previous winning combinations and identifying any recurring patterns or numbers that are more likely to appear.

## 3. Is there a specific order in which the numbers should be placed on the two rows?

Yes, the order of the numbers can play a crucial role in determining the success of your strategy. It is recommended to place the numbers in a balanced and symmetrical manner, rather than randomly, to increase the chances of a winning combination.

## 4. Can this strategy be applied to all types of games?

While this strategy can be applied to many games that involve numbers, it may not work for every game. It is important to understand the rules and patterns of the specific game you are playing before implementing this strategy.

## 5. Are there any disadvantages to using this perfect strategy?

One potential disadvantage of using this strategy is that it does not guarantee a win. While it can increase your chances of winning, there is still an element of luck involved. Additionally, this strategy may not work for every game and can be time-consuming to analyze and implement.

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