QuestionCreate a 3x3 magic square using 9 of the numbers: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. Explain your solution and strategies.
Studdy Solution
STEP 1
Assumptions1. We are creating a3x3 magic square.
. We are using nine of the ten numbers from20 to29.
3. The numbers in all rows, all columns, and the two diagonals must have the same sum.
STEP 2
First, we need to calculate the sum of the numbers from20 to29, excluding one number. This will give us the total sum of the numbers we are using in the magic square.
STEP 3
We know that the sum of each row, column, and diagonal in a3x3 magic square is equal to one third of the total sum of the numbers in the square. Therefore, we can calculate the magic sum (the sum of each row, column, and diagonal) by dividing the total sum by3.
STEP 4
We know that the center number in a3x3 magic square is always equal to the magic sum. Therefore, we can select a number from the given list that is close to the magic sum as the center number.
STEP 5
We can then arrange the remaining numbers in the square in such a way that the sum of each row, column, and diagonal equals the magic sum. This may require some trial and error.
STEP 6
After trying different combinations, we find that excluding29 from the list of numbers and arranging the remaining numbers as shown below results in a magic squareIn this square, the sum of each row, column, and diagonal is72, which is the magic sum.
Strategies used1. Calculation of the total sum and magic sum.
2. Selection of the center number based on the magic sum.
3. Trial and error to find the correct arrangement of numbers.
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