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Whether the message gets added to the victory text. If you don't tell her about the dog's death or give her the corpse, she will have her usual dialog "Me sayz thanks for getting back me puppy."

Wish immediately - works
Wish after the time limit without generating last puppy cave level - works
Wish after generating the last puppy level after the time limit - fails
Wish after seeing the...

Sadly, a wished for cute dog doesn't seem to give the high score line (brought back joy into the life of a tiny girl). Wished for raider lord might work, since the high score line is triggered by...

Tested a character with 84 PV. Got raiders on the 4th encounter, and 26/100 plains encounters were roving raiders. This lines up pretty well with what TB has said: "After having received the quest...

You should do some chaos knight runs! Find an altar and a source of fire resistance, then try to do both raider and puppy quests. >:D

For bonus points, get the raider encounter on the hills square...