Why wouldn’t you change your questions based on the responses you have already gotten? Also, you are assuming that the target has at most one grenade, an assumption which I think is valid.
I agree that asking logically equivalent questions or self-referential questions breaks the spirit of the rules, but asking questions which are subsets of previous questions is not.
Given that case 1 is not having a grenade, and case 2-4 are having grenades of each color, the questions could go like this:
Case 1 or 2? Case 3 or 4? Case 2 or 3?
000: Case 1? (yes 1, no 4) 001: Case 2? (yes 2, no 3) 010: Case 1,2,3? (yes 3, no 4) 011: Case 1,2,3? (yes 3, no 4) 100: Case 2,3,4? (yes 2, no 1) 101: Case 2,3,4? (yes 2, no 1) 110:Case 1? (yes 1, no 4) 111:Case 2? (yes 2, no 3)
This line uses what I consider a cheap trick of asking the same question twice in a row, because once “3 or 4” is known, “2 or 3?” and “1,2, or 3?” both simplify to “3?”
I agree that the assumption that you wouldn’t change your questions based on the responses is not a reasonable one, but I realized that I had made it after I came up with my argument, and decided to share it anyway in case people found it interesting.
If later questions are allowed to reference earlier answers by the interrogee, you could get all the benefit of changing your questions by multiplexing among possible later questions based on their answers to earlier questions, all within one question. For example: if your first question was “is the ball red”, and if they say yes your next is “is the ball blue”, and if they say no you say “is the ball green”, your second question would always be be “Is it true that you just said ‘yes’ and the ball is blue or that you just said ‘no’ and the ball is green?”
You can also deal with the ruleset where they could have a grenade of one of three colors, or they could have nothing with my method of dealing with 4 possible colors, by replacing all references to “pink” with “no grenade”.
Why wouldn’t you change your questions based on the responses you have already gotten? Also, you are assuming that the target has at most one grenade, an assumption which I think is valid.
I agree that asking logically equivalent questions or self-referential questions breaks the spirit of the rules, but asking questions which are subsets of previous questions is not.
Given that case 1 is not having a grenade, and case 2-4 are having grenades of each color, the questions could go like this:
Case 1 or 2? Case 3 or 4? Case 2 or 3?
000: Case 1? (yes 1, no 4)
001: Case 2? (yes 2, no 3)
010: Case 1,2,3? (yes 3, no 4)
011: Case 1,2,3? (yes 3, no 4)
100: Case 2,3,4? (yes 2, no 1)
101: Case 2,3,4? (yes 2, no 1)
110:Case 1? (yes 1, no 4)
111:Case 2? (yes 2, no 3)
This line uses what I consider a cheap trick of asking the same question twice in a row, because once “3 or 4” is known, “2 or 3?” and “1,2, or 3?” both simplify to “3?”
I agree that the assumption that you wouldn’t change your questions based on the responses is not a reasonable one, but I realized that I had made it after I came up with my argument, and decided to share it anyway in case people found it interesting.
If later questions are allowed to reference earlier answers by the interrogee, you could get all the benefit of changing your questions by multiplexing among possible later questions based on their answers to earlier questions, all within one question. For example: if your first question was “is the ball red”, and if they say yes your next is “is the ball blue”, and if they say no you say “is the ball green”, your second question would always be be “Is it true that you just said ‘yes’ and the ball is blue or that you just said ‘no’ and the ball is green?”
You can also deal with the ruleset where they could have a grenade of one of three colors, or they could have nothing with my method of dealing with 4 possible colors, by replacing all references to “pink” with “no grenade”.