Respuesta :
Explanation:
We can demostrate this claim by using global induction.
First, if the board has only one row, then you eat the non poissoned block and you win.
If it is a 2x2 row, then you have to eat the bottom right block, and in his next move, your opponent will be forced to eat only one block, leaving only 2 on the table. Then you eat the non poissoned one and you win.
Lets suppose that you have a winning strategy for a 2xk board, for k < n. If the board has dimensions 2xn, then
- You eat the bottom right corner block
- If your opponent eats exactly the block next to it, then you apply the winning strategy and its done.
- If your opponent eats a right-side block, then you can always eat the left-side block immediately below to it, leaving the board in a similar state than after your first move. Then you keep applying the same strategy until your opponent cant eat right side blocks.
- If your opponent instead eats a left side block, then the board will turn into a 2xj board and you can use a winning strategy (which exists due to the inductive hypothesis).
This way, you will always have a winning strategy by being first.
The proofing that the first player has a winning strategy in the game of Chomp will be done through strong induction.
How to proof by strong induction?
From the information, the loser will be the person who eats the poisoned cookie. Let P(n) be the first player that has a winning strategy for the game.
Basis step n = 1
The first player eats the non poisoned cookie and then the second player will eat the poisoned cookie which means the first player wins. Thus P(1) is true.
In conclusion, the first move of the first player is to eat the cookie in the bottom right corner.
Learn more about strong induction on:
https://brainly.com/question/15690473
