And things to consider a bit of reflection.
First when Toshiki Inukai was found and retrieved safely by Akasaka and Oishi.
Second, the analogy about the water's reflection and the moon casted by Rika's mature side.
Spoiler:
Exactly, I did not get much of it, that's why I need to rewatch the episode again, however, this what I understood.
1. She ends her cryptic analogy that if she throws the pebble into the water and causes ripples, then her whole effort would not have become in vain.
In that last line could she have meant explaining each of the murders that will follow throughout the course of the next five years to Akasaka. If that's the case, then it makes sense that Rika did challenge her fate or attempt to challenge after all.
By passing the knowledge about what was coming up to Hinamizawa in the future, Rika averted the most infamous of all deads- oblivion, that is to be permanently forgotten.
At the epilogue to Himatsubushi-hen, Akasaka cannot shaken off his experiences about Hinamizawa and neither Rika. He took the chance to talk Oishii about it, and the former inspector also became immersed in the topic; Oishii wanted to solve the murder mysteries before his retirement but due to the gas explosion that occurs in this scenario will never happen.
If it was Rika's last wish to leave her legacy on someone else, then I could interpret that Rika did not want the mystery remain hidden and eventually forgotten, neither things at Hinamizawa ended just like they did in the last question arc.
What relieves me most with a sense of joy....