POW Answer – True, False, & Random

This is the answer to last week’s Problem of the Week.  The thing that made that problem so difficult is that you must account for RANDOM. Therefore, the first goal is to first determine at least one entity who cannot possibly be RANDOM. Thusly, the first question which will be posed to the middle entity can be something like “if I were to ask you if the entity on the left is RANDOM, would you say da?”

If talking to TRUE or FALSE and RANDOM is on the left, the answer given will be “da“.  If talking to TRUE or FALSE and RANDOM is on the right, the answer given will be “su“. If talking to RANDOM, either “da” or “su” could be given as the answer.

After this question, if the answer received is “da“, you know that you are either talking to RANDOM, or RANDOM is to the left.  Therefore you should direct your next question to the person on the left.  If the answer received is “su“, you know that you are either talking to RANDOM, or RANDOM is to the right.  Therefore you should direct your next question to the person on the left.

You will notice that with just the first question, we have made sure that our next question will not be directed to RANDOM.  Now the purpose of the next question is to determine if the second person is TRUE or FALSE.  The next question can be “does da mean yes?”

• If talking to TRUE, the response will be “da“:
• If you replace da with yes…
• The question would be “does yes mean yes?”
• TRUE would answer “yes” (same as the bold word used).
• If you replace da with no…
• The question would be “does no mean yes?”
• TRUE would answer “no” (same as the bold word used).
• If talking to FALSE, the response will be “su“:
• If you replace da with yes…
• The question would be “does yes mean yes?”
• FALSE would answer “no” (opposite of the bold word used).
• If you replace da with no…
• The question would be “does no mean yes?”
• FALSE would answer “yes” (opposite of the bold word used).

Now that we have determined who the second entity is, it is time to ask a question that will identify who RANDOM is.  This last question will need to be similar to the first in that it will need to produce the same answer from both TRUE or FALSE since you don’t know what da or su means.  The question can be “if I were to ask you if the first entity I talked to was RANDOM, would you say da?”

• If the response is da, the first entity is RANDOM.  This can be proven by substitution of da for either yes or no:
• QUESTION:  If I were to ask you if the first entity I talked to was RANDOM, would you say yes?
  ANSWER:  yes
• QUESTION:  If I were to ask you if the first entity I talked to was RANDOM, would you say no?
  ANSWER:  no
• If the response is su, the entity with whom you didn’t speak is RANDOM:
• QUESTION:  If I were to ask you if the first entity I talked to was RANDOM, would you say yes?
  ANSWER:  no
• QUESTION:  If I were to ask you if the first entity I talked to was RANDOM, would you say no?
  ANSWER:  yes