Battle Royale test

Hi people,

I'm reading Battle Royale and I've come to the point where Shougo tells Shuuya and Noriko about the psycho test or whatever, he shows them these characters, first: 机 (tsukue) desk, then 桜桃 (outou) cherry tree or something similar, and lastly 銃殺 (jyuusatsu) murder by firearm. This last one seems to get a strong reaction from our protagonists, and Shougo says it was used to know if a child had psychological problems.

Can someone explain how it works and why are those 3 words related?

here's a link to the manga http://mangafox.me/manga/battle_royale/v12/c095/12.html

image related, the three words in the manga

I haven't the foggiest because I've never read the manga but latter pages obviously show some kind of shooting or event that happened in the past. 机 obviously has some connection to school, 桜桃　(さくらんぼう) might be either a seasonal connection, or something to with a character or setting. 銃殺 is pretty obvious.

Other than that, building associations between words, 桜桃　might cause someone to associate 咲く乱暴, which then leads to 銃殺 but I really have no idea. There might be a kanji connection, looking at radical and associated meaning but again, no clue.