In sumin(n), you choose the number that is smallest of x and y, in sumax(n) you choose the biggest.

Like this:

     0    1	2	3	4	5	6

6	-	6	6	6	6	6	6

5	-	5	5	5	5	5	6

4	-	4	4	4	4	5    6

3	-	3	3	3	4	5    6

2	-	2	2	3	4	5    6

1	-	1	2	3	4	5    6

0	-	-	-    -    -    -    - 

the k*k that contain the digit 1 are:

1, 16, 81, 100, 121, 144, 169, 196, 361, 441. (Only 10 numbers here)

So there are 11 digits 1 for the squares of numbers between 0 and 25. (Counts it as 11, because 121 contains 1 two times)