A mathematical solution

 In a combinatorial analysis 2 students will be 2, 3 will be 6, so you can see that it's a sum of the value of students -1 like 30 will be 29+28+...+1, so taking the calculator we'll add up to give 36 1+2+3+4+5+6= gave 21, adding+7=28, +8=36 so it's 8+1 which is 9.

Is that if we gonna make groups of 2 in a number of students see that you got one number and combine with all so if:

1,2 only combination 1-2    1

1,2,3 you have all the combinations for till 2 + for 3 that is it by 1 and one so add this to the 1st result

1,2,3,4 and you only have to combine for 4 and add to the previous, 

when you got 90 you gonna notice that the 90 gona combine with all and all is 1 to 90 less the 90 itself,

so groups of 2 are combinations that gonna subtract the own number because it need combine with all.

So the conclusion isn't miracle or because mathematical brains works in reverse.

Rute Bezerra de Menezes Gondim