Solution 1 with 2 as center
9 4 8
6 2 5
1 3 7
13 squares { 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 625, 729, 961 }
Strategy:
I first write down the all 3 digits squares then I look for the 3
digit squares with a most solid center. means a maximum of 3 digits
squares with common center number. I found there are 4 these types of
squares {324, 625, 529, 729} where the common center is 2. so I made 2
is my center number and write down all the 3 digits squares. then I
tried to cover the other 3 digits squares by rearranging them. then
finally I look for all 2 digit squares and be able to get them mostly
except 81. Also, one more thing {169 and 961} is also a good combo so
don't miss it. if you see the 3 digit square list below that we can
use, we can clearly see that 2 makes the most solid center so the most
solid solution, after it 6 and 8 can give a better result.
Possible 3 digit squares we can use with solid centers.
1. {324, 529, 625, 729} we can either use 529 or 729 so 3 left
2. {169, 361, 961 } {we can either use 361 or 961 so 2 left}
3. {289, 784 } {we can use both}
4. {841}{196}{256}{576} {4,9,5,7 with center we will get only 1 square}
as you can see above we can use 3 of 3 digit square with 2 as center that will give us best solution. 729 is giving better solution than 529 because with 729 we are getting advantage of using one more 3 digit square 625 which is not possible with 529 because we can either use 529 or 625.
Solution 2 with 2 as center
5 7 8
3 2 4
1 6 9
same strategy 12 squares { 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 529,
961 }
Solution 3 with 8 as center
2 7 1
5 8 6
3 4 9
Another 12 squares{ 1,4, 9, 16, 25, 49, 64, 81,169, 196, 289, 784 }
Solution 4 as 6 as the center.
1 5 7
8 6 2
3 4 9
12 squares same strategy { 1 ,4, 9, 16, 25, 49, 64, 81,169, 729, 961 }