You have three sums of 17 each, for a total of 3 x 17 = 51.
Yet, if you sum all the digits from 1 through 9, you only get 45.
This means that there is an overlap of 6 (51 - 45 = 6).
The overlap occurs because the three end numbers are each counted twice.
The three numbers that total to 6 are 1, 2, and 3.
So, the sum of the three corner digits is 6.