Glantri vs. the End of the World
I mumble to myself, thinking quickly.
"Logic puzzles, I've done these hundreds of times. Think quick Mike, think!"
"Ok, so the Wind King can't be the liar. As there is only one liar, and if the Water King is telling the truth and is the youngest, the Wind King can't be younger.
Likewise, the Earth King can not be the liar. If the Fire King is not lying and is thus the oldest, the Earth King is honest is saying he is not the oldest.
So that leaves the Water King or Fire King as the liars.
If the Fire King is lying, we know that the Water King is the youngest. We know that the earth king is not the oldest, and neither is the Fire King since he is lieing, so the Wind King is the oldest in that scenario. But The order could be Water->Earth->Fire->Wind or Water->Fire->Earth->Wind. In both those scenarios there is only one liar, and that liar is the Fire King. As such I must assume the fire king is not the liar, as it doesn't yield a finite answer.
So that leaves us with the Water King lying. So We know Fire is the oldest, Water king is not the youngest, and Wind is older than Water. So the order must be Earth->Water->Wind->Fire.
In that case, Fire is telling the truth, he's the oldest. Wind is telling the truth, he's older than Water. Water is lying, he's not the youngest. And Earth is telling the truth, as he's not the oldest. Further, it's finite, so I must assume I have missed something, and the secondary clues pointed towards Water lying instead of Fire."
With the I light the candles in the order of Earth->Water->Wind->Fire. Hopefully that works, and I'll press on.