Formulate the 3 x 3 game as a search problem, i.e. define the states, the moves, etc.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Moving Magic Square is the name of a game that is based on the concept of a magic square. A
magic square is any square array of numbers, usually positive integers, in which the sums of
the numbers in each row, each column, and both main diagonals are the same. For example,
the 3 x 3 square in Table 1 is a magic square because the sum of every row, every column and
the two diagonals is 15.
Table 1
6 18
753
294
The game, Moving Magic Square, is played on any n x n grid containing positive integer
numbers from 1, ..., n². The number n² is the movable number. You can move the number n²
in one of four directions (up/down/left/right), and swap n² with the number that is currently
occupying that cell. The player wants to move the number n² to reach a goal state such that the
sum of the n numbers in every row, column, and both diagonals is equal to k. There are multiple
states that satisfy this condition, and you can stop the game when you find the first goal state.
Transcribed Image Text:Moving Magic Square is the name of a game that is based on the concept of a magic square. A magic square is any square array of numbers, usually positive integers, in which the sums of the numbers in each row, each column, and both main diagonals are the same. For example, the 3 x 3 square in Table 1 is a magic square because the sum of every row, every column and the two diagonals is 15. Table 1 6 18 753 294 The game, Moving Magic Square, is played on any n x n grid containing positive integer numbers from 1, ..., n². The number n² is the movable number. You can move the number n² in one of four directions (up/down/left/right), and swap n² with the number that is currently occupying that cell. The player wants to move the number n² to reach a goal state such that the sum of the n numbers in every row, column, and both diagonals is equal to k. There are multiple states that satisfy this condition, and you can stop the game when you find the first goal state.
1. Formulate the 3 x 3 game as a search problem, i.e. define the states, the moves, etc.
Transcribed Image Text:1. Formulate the 3 x 3 game as a search problem, i.e. define the states, the moves, etc.
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