|Spoiler Inside: Solution to Puzzle||SelectShow>|
A magic square with values one to nine has each row, column, and diagonal sum to 15. With this magic square, since each number is five higher, the sum must be 15 higher: 30.
If the corner values were all even, the other values would all have to be even to have rows, columns, and diagonals summing to 30. Therefore, the corner values are odd. There are four corners and four odd values. Therefore, the non-corner values are even.
This means that only 11 and 14 in the other clues are possible values for the squares specified.
In order that the middle row and middle column both sum to 30, the center square value must be 10.
From there, it is just a matter of filling in the third square in some row, column, or diagonal that has two values.
The solution: top row: 13, 6, 11; middle row: 8, 10, 12; bottom row: 9, 14, 7.