arrange the numbers 8 to 16 in the square so that the sum of each row (across, down, diagonally) will always be 36. ply help my daughters.
The basic magic square using 1-9
816
357
492
sums to 15
By raising all the values by 7, you use the numbers 8-16, and each row/column/diagonal is raised by 3*7=21, so they sum to 36
a web search on magic squares will reveal many articles on their construction. Odd-order squares are particularly easy.
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To solve this problem, we need to arrange the numbers 8 to 16 in a square grid so that the sum of each row (across, down, diagonally) is always 36.
Let's break down the process into steps:
Step 1: Start by drawing a 4x4 grid. Label each cell with variables A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, and P.
A B C D
E F G H
I J K L
M N O P
Step 2: Assign the numbers 8 to 16 to these variables. You can start by placing the numbers 8, 9, 10, and 11 in the first row, as no other number can be greater than or equal to 12.
Step 3: Now, consider how the numbers in the second row (E, F, G, H) can be arranged. Start by placing the number 16 in one position and consider the sum of the remaining three cells. Since each row sum must be 36, subtract the known values from 36 and divide by 3 to find the average value for each cell. If any cell contains a number higher than 16 or lower than 8, it is not a valid solution.
Step 4: Once you have determined the positions for the remaining numbers 12, 13, 14, and 15, proceed to arrange the numbers in the third and fourth rows using the same method.
Step 5: Check all the row sums (across, down, diagonally) to ensure they all equal 36.
Remember to explore different arrangements and keep trying until you find a solution that satisfies the condition.
It's important to note that there may be multiple valid solutions to this problem.
716
359
482
adds to 140