A Logical Explanation of the Solution to the Enigmatic ‘Prisoner Hat Riddle’

In a TED-Ed video “Can you solve the prisoner hat riddle?” Alex Gendler gives a logical solution to the enigmatic prisoner hat riddle. The prisoners in the story are each randomly assigned a black or white hat and are forced to stand in a row, only able to see the prisoners in front of them. They must correctly identify the color of their own hat, but can only say the words “black” and “white.”