

Spoiler
8 Injustices + 1 Chief Injustice = 9 handshakers. Each handshaker shakes 8 people’s excluding themselves, but you musn’t count the same handshake twice for each person.
The first shakes 8 times and is done. The second shakes 7 times because the 8th was already included in the count of the first person…
8+7+6+5+4+3+2+1=36
Yes absolutely, but that is only faster when n is large enough to become unwieldy, or the process needs to be repeated for various numbers of shakers. When doing it in your head for a single low number question this is where I landed.