Odd, put on the helm and troll and got 10 hides in 96 turns, also got 9 doodles. Not sure if that is meaning they're included in the quest or if it's just chance.
EDIT: Decided to eat and drink, 424 turns later I have another 49 doodles and 49 hides. It definitely looks to me like both are necessary for the quest, but how. Yeti Diddles? Hairy puzzle? I tried both in a variety of ways, no help there.