The LINQ query for square nodes is a good move, but checking the sum equal to 45 is not applicable to similar tasks. Here is a test that your algorithm does not perform, you can check.

new object[] //All rows,colums and nodes have sum 45 from 1+2+3+4+5+6+7+8+9
{
"Try again!",
new int[][]
{
new int[] {1,2,2,2,2,9,9,9,9},
new int[] {2,9,9,2,1,9,2,2,9},
new int[] {2,9,9,2,9,9,2,2,1},
new int[] {9,2,2,9,9,9,1,2,2},
new int[] {9,1,2,9,2,2,2,9,9},
new int[] {9,2,9,1,2,2,2,9,9},
new int[] {2,9,1,9,9,2,9,2,2},
new int[] {2,9,2,9,2,1,9,9,2},
new int[] {9,2,9,2,9,2,9,1,2},
},
},

The first word should always be with the upper symbol, I do not see something here as it is controlled, do not tell me?