Viral logic test from Brazil

The 17th annual Brazilian Olympiad featured an incredibly tricky logic puzzle that went viral on social media. Thanks to Guilherme who suggested and translated the problem from Portuguese to English!

Pinocchio problem discussions
https://ultimosegundo-ig-com-br.trans...
https://sivtelegram.media/students-ma...
  / a_question_about_pinocchio_what_is_your_op...  
https://brainly.com.br/tarefa/52854041

Pinocchio illustration
https://en.wikipedia.org/wiki/File:Pi...

See Bram28 explanation for vacuously true
https://math.stackexchange.com/questi...

Wikipedia vacuous truth
https://en.wikipedia.org/wiki/Vacuous...

Wikipedia truth table
https://en.wikipedia.org/wiki/Truth_t...

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