Need help or answer on easy composites and primes math question

Algebra
Tutor: None Selected Time limit: 1 Day

Place the digits 1 through 9 a 3x3 grid so that each row forms a three-digit composite number and each column forms a three-digit prime number. Each digit must be used once and only once on the grid. Explain how you found your solution. How many solutions can you find? 

Jun 1st, 2015

There is a general, very simple, algorithm for generating any magic square which has an odd number of rows/columns as follows:

  1. Start in the middle of the top row and enter 1.
  2. Move Up 1 and Right 1 wrapping both vertically and horizontally when you leave the grid *(see note below).
  3. If that square is empty enter the next number; if the square is not empty put the next number underneath the last number you entered.
  4. Repeat 2&3 until the grid is complete. All rows, columns and the two diagonals will sum to the same value.

Here is the 5x5 square:

17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9

As the square square is symmetric there are eight symmetries. You can also get these symmetries by a simple variation of the start square and direction used in step 2.

*Note: So as you are in the middle of the top row on the first move you want to place the next number in the next column of the row above. The row above does not exist so move to the last row of the square in the same column. If you were in the last column you would move to the first column. If you look at the example of the 5x5 at number 15. The next position is the square up and to the right of 15 which wraps on both the row and column to point to the lower right square which has 11 in it. As that square is not empty we placed 16 underneath 15.


Jun 1st, 2015

Can you try para-phrasing that? I didn't understand it. Plus I'm on a 3 by 3 grid

Jun 3rd, 2015

Can you try para-phrasing that? I didn't understand it. Plus I'm on a 3 by 3 grid

Jun 3rd, 2015

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