rearrange the numbers in a 4 x 4 array so that each row column and diagonal equal 10
using numbers 1-4
To rearrange the numbers in a 4 x 4 array so that each row, column, and diagonal equals 10, you can follow these steps:
Step 1: Understand the problem
Start by visualizing the 4 x 4 array. Each cell in the array can contain a number from 1 to 4. The goal is to find an arrangement where the sum of each row, column, and diagonal equals 10.
Step 2: Analyze the conditions
In this problem, there are several conditions that need to be met:
a) Each row, column, and diagonal must sum up to 10.
b) Each number from 1 to 4 must appear only once in each row and each column.
c) The values in the two main diagonals (top-left to bottom-right and top-right to bottom-left) must also sum up to 10.
Step 3: Start with fixed values
To simplify the problem, we can fix the values in certain cells and find arrangements based on these fixed values. Since each row, column, and diagonal sum up to 10, we can determine the fixed values by considering the sum of the remaining cells in each row, column, and diagonal.
Step 4: Find the fixed values
Given that each row must sum up to 10, we can start with the first row and fix the first number as 1 to ensure the sum is 10. Then, we can calculate and fix the values for the other cells in the first row: 1 + a + b + c = 10, where a, b, and c represent the remaining three numbers in the first row.
Similarly, we can fix the first number in the second, third, and fourth rows based on the remaining sums required for each row.
Next, we can fix the first value in each column based on the remaining sums required for each column.
Step 5: Arrange the remaining values
After fixing the values in specific cells, we can arrange the remaining values in the empty cells. This can be done using trial and error or by applying additional logical deductions based on the fixed values and the conditions of the problem.
Step 6: Check the solution
Once you have arranged all the numbers in the array, verify that each row, column, and diagonal indeed sum up to 10. If the solution does not satisfy any of the conditions, go back to Step 5 and try a different arrangement.
By following these steps, you should be able to rearrange the numbers in a 4 x 4 array such that each row, column, and diagonal equals 10.