You are a knight tasked with rescuing the King's daughter. The princess is being held captive by a band of evil dragon pirate monks. You've been debriefed with prior intelligence gathered through reconnaissance to inform your journey. To reach her prison cell you must pass through two consecutive rooms, each guarded by a single dragon. Thankfully, you need not fight the dragons alone. You've managed to sneak into the band's incubating chamber where they keep their dragons in suspended animation. The dragons are grouped into seven weyrs1. Each weyr has a corresponding summoning stone used to summon a dragon out of suspended animation. The stones are labeled as follows:
A: 2, 14, 17
B: 7, ?, 16
C: 13, ? 15
F: 8, ?, 6
G: ? 11, 18
Each weyr (indicated by its letter) contains three pairs of dragons. No two pairs of dragons share the same class amongst the seven weyrs, and each pair always shares the same class. The three numbers next to each weyr represent the class of each pair. A class represents a dragon's strength. Classes range from 1 to 21, with a class 21 dragon being the strongest.2
The summoning stone is used to summon a dragon from its weyr. Each dragon from that weyr has an equal probability of being summoned. Only one dragon from a weyr can remain summoned at a time. The outcome of each summon is independent of the last.
You notice that some of the numbers on the stones are unreadable (indicated by a "?"), and two stones are missing altogether.
Each day, the band of dragon pirate monks randomly selects two summoning stones and randomly summons a dragon from each stone into a room. You do not know which dragons from the missing weyrs currently guard the two rooms.
In order to get past the dragons and save the princess, you plan to steal one of the remaining five summoning stones. For each room you'll summon a dragon. If all goes well, your dragon will be of higher class and will defeat the other dragon3. The dragons cannot fit through the doors, so after (hopefully) defeating the first dragon, you'll return it back into suspended animation and proceed through the next door, where you'll summon another dragon. Each stone only has enough magic for two summons, and you can only choose one stone.
The good news: before you began your quest, Intelligence had indicated that, should you choose the best stone, your chance of defeating the first dragon would be greater than 50%.
The bad news: The chances of defeating both dragons is still slim.
Which stone should you choose?
Bonus: What is the probability of defeating both dragons with this stone?
- A weyr /ˈwɪər/ is a collection of dragons.
- For example: Weyr A contains a pair of class 2 dragons, a pair of class 14 dragons, and a pair of class 17 dragons.
- The dragons will fiercely protect their summoner and are hostile to other dragons