The induction puzzle goes as follows:
‘The King called the three wisest men in the country to his court to decide who would become his new advisor. He placed a hat on each of their heads – such that each wise man could see all of the other hats- but none of them could see their own. Each hat was either white or blue. The king gave his word to the wise men that at least one of them was wearing a blue hat – in other words there could be one two or three blue hats but not zero. The king also announced that the contest would be fair to all three men. The wise men were also forbidden to speak to each other. The king declared that whichever man stood up first and announced the color of his own hat would become his new advisor.’
Roboticists at the Ransselaer Polytechnic Institute adapted it for a trio of robots – two of which were told they had been given a ‘dumbing pill’ which prevented them from talking before all three were asked which one was still able to speak.