A 'Game of Thrones' Maths Puzzle
Four prisoners escape from the dungeons at King’s Landing and head for the Wall; a distance of 700 leagues. The Maester travels 1 league in the first day, then each subsequent day, doubles the distance he travelled the previous day. The Whore travels 50 leagues each day. The Knight travels 80 leagues each day, and 20 leagues each night. The Squire travels 350 leagues the first day, then each subsequent day, travels half the distance he travelled the previous day.
Two days after the prisoners escape, the Mountain is sent out to hunt them down and kill them. He travels 100 leagues each day. The Maester has a 5% chance of talking the Mountain out of killing him. The Whore has a 20% chance of seducing the Mountain and escaping death. The Knight has a 45% chance of defeating the Mountain in combat. The Squire has a 70% chance of evading the Mountain. All prisoners risk being attacked and killed by wolves; a 5% chance each day, and a 25% chance each night. If any prisoner reaches the Wall they ’take the black’ and live out their days in the Night’s Watch.
Assuming all prisoners have enough food, water and clothing, which of them is guaranteed to die before they reach the Wall, and how will they die?