There are three people: Amanda, Bill, and Cindy.

One of them has a favourite colour of blue, one of them has a favourite colour of green, and one of them has a favourite colour of red. They do NOT know the favourite colours of the others.

One of them always tells the truth, codename "True". One of them always lies, codename "False". One of them uses secret coin tosses to determine how to answer (heads = affirmative, tails = negative), codename "Random". Each one also knows the codename of the others.

Each of them speaks either Jaism or Daism.

In Jaism, "Ja" means "Yes" and "Da" means "No".

In Daism, "Da" means "Yes" and "Ja" means "No".

They understand all of your questions regardless of the language of the question, but they will only respond in their language. They do NOT know which language the others speak.

Your goal is to determine the favourite colour of True, the favourite colour of False, and the favourite colour of Random.

In order to do so, you may ask a series of yes-or-no questions. Each question can be posed to exactly one person. You are allowed to ask the same person multiple questions. If you ask an invalid question (a question that is unanswerable by the person asked), the game immediately ends in failure.

What is the smallest number of questions required to form a guaranteed solution? A guaranteed solution must work 100% of the time, regardless of the favourite colour, codename, or language of Amanda, Bill, and Cindy, as well as the results of Random's coin tosses.

Shortly after market close, I will resolve to the number indicated by the proposed solution with the lowest number of questions to which I cannot find a valid counterexample.

• Update 2025-07-18 (PST) (AI summary of creator comment): The creator has indicated they may resolve this market before the scheduled close date under a specific condition:

  • If there is virtual agreement among participants that a particular answer is correct and has no counterexamples, while all proposed solutions requiring more questions do.