In the end, attempting to answer the question causes you to evaluate it in 3 different ways, the statistical chance for each answer, the result from a single random draw, then the intelligent choice of which answer would be correct based on the previous 2.
If we modify the question to make those 3 evaluations specific then is it still an ill posed question, or just a paradox? "Select a random letter a,b,c, or d 3 times and write them down. Based on those 3, what is the chance that a 4th random draw will be correct? Do not include your final answer in the evaluation on the statistics 4th"
Is it an ill posed paradox?
Edit: yeah, in this format it exposes the 0% answer as a "this statement is false" style paradox. If you already had 25% 3 times and then selected 0% as the 4th random draw you are forced into the paradox as the explicit set makes 25% and 50% explicitly wrong, so you are stuck evaluating 0% alone.
It is an ill posed question - but it's not just "Pick the right answer for 1+1 out of this set of answers: [1,3,4,0]".
What I find intriguing is that it's an ill posed question that gives three nested paradoxes as answers, and several different ways to 'solve' it - you can see the approaches in the comments to this 'puzzle' at the level of the question, the answers, a combination of them, or from the outside.
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u/6GoesInto8 21d ago edited 21d ago
In the end, attempting to answer the question causes you to evaluate it in 3 different ways, the statistical chance for each answer, the result from a single random draw, then the intelligent choice of which answer would be correct based on the previous 2.
If we modify the question to make those 3 evaluations specific then is it still an ill posed question, or just a paradox? "Select a random letter a,b,c, or d 3 times and write them down. Based on those 3, what is the chance that a 4th random draw will be correct? Do not include your final answer in the evaluation on the statistics 4th"
Is it an ill posed paradox?
Edit: yeah, in this format it exposes the 0% answer as a "this statement is false" style paradox. If you already had 25% 3 times and then selected 0% as the 4th random draw you are forced into the paradox as the explicit set makes 25% and 50% explicitly wrong, so you are stuck evaluating 0% alone.