Question

Make a magic square using only first nine odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17. (In a magic square, the numbers in each row, in each column, and along each diagonal have the same sum.)

Answer 1

To create a magic square using the first nine odd numbers (1, 3, 5, 7, 9, 11, 13, 15, 17), arrange them in a 3x3 grid such that the sum of each row, column, and diagonal is the same.

Step-by-step explanation:

To create a magic square using the first nine odd numbers (1, 3, 5, 7, 9, 11, 13, 15, 17), we can arrange them in a 3x3 grid such that the sum of each row, column, and diagonal is the same. Here is an example:

9151135731117

In this magic square, the sum of each row, column, and diagonal is 25. You can try creating other magic squares with the given odd numbers by rearranging them in different ways while maintaining the sum.

Answer 2

Answer:
`\left[\begin{array}{ccc}11&13&3\\1&9&17\\15&5&7\end{array}\right]`

Step-by-step explanation:

A magic cube is something like:

`\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]`

Where the numbers that we must use are:

1, 3, 5, 7, 9, 11, 13, 15, 17

If we take the addition of those 9 numbers, we get 81.

Now, we divide it by 3 (the number of numbers in each row or column) and get:

81/3 = 27

so the sum in each row, column and diagonal must be 27.

1 + 9 + 17 = 27

13 + 11 + 3 = 27

5 + 7 + 15 = 27

9 + 13 + 5 = 27

You can keep playing with this, and then start forming our number cube, some of the hints tat we can use is that the median of the group is 9, so it must be in the middle of the cuve, and the extremes, 1 and 17, must be in the same column or row as 9.

so we start with:

`\left[\begin{array}{ccc}x&x&x\\1&9&17\\x&x&x\end{array}\right]`

and start to fill the empty spaces, now we can use that

1 + 11 + 15 = 27 and get:

`\left[\begin{array}{ccc}11&x&x\\1&9&17\\15&x&x\end{array}\right]`

now for the diagonals:

11 + 9 + 7 = 27

15 + 9 + 3 = 27

`\left[\begin{array}{ccc}11&x&3\\1&9&17\\15&x&7\end{array}\right]`

and for the last one:

11 + 3 + 13 = 27

15 + 7 + 5 = 27

`\left[\begin{array}{ccc}11&13&3\\1&9&17\\15&5&7\end{array}\right]`