Kingship is definitely precious
In 2099, Petrov de Laurence, the king of Portugal is finally deposed. The five remaning earls argue about which one of them would be the king, and which one would be a treasurer.
• Alain will be satisfied only if Doodle or Elena is the treasurer.
• Billy will be satisfied only if Clare is the treasurer.
• Clare will be satisfied only if Doodle is either the king or treasurer.
• Doodle will be satisfied only if Alain is the king or the treasurer.
• Elena will be satisfied only if Alain is not the king.
It is not possible for all of the five earls to be satisfied, so in the end, they appoint the king and treasurer so that three earls are satisfied.
Who becomes the king?
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1 solution
Two of the earls will not be satisfied, leaving three satisfied.
We can see that Alain and Clare have similar wants. (Both are satisfied if Doodle is the treasurer.)
If Doodle is the treasurer, we will leave Alain and Clare satisfied and Billy unsatisfied. This leaves us with Doodle and Elena.
Their wants contradict each other, as Doodle is the treasurer. Leaving just Alain to be crowned king.
Alain = Satisfied (King)
Billy = Unsatisfied
Clare = Satisfied
Doodle = Satisfied (Treasurer)
Elena = Unsatisfied
This meets the criteria, so therefore Alain was crowned king.