A Simple Math Puzzle

8 Comments »

1. 

   Zach Barnett August 24, 2012 at 11:00 am - Reply

   It’s a bad question with no right answer. Proof:

   Let’s assume there is at least one correct answer.

   First, assume there is exactly one right answer to the question. If this is so, then the probability of picking it at random is 25%, since 1/4 = .25. But if this is so, then there are actually two right answers (A) and (D). But we are assuming there is only one. Contradiction. There can’t be just one.

   So there must be more than one right answer. There could be two, three, or four.

   Suppose there are two. Then the probability of picking one of them at random is 50%. But if this is so, then there is only one right answer (B). Contradiction.

   Suppose there are three right answers. Then the probability of picking one of them at random is 75%. But then there are no right answers. Contradiction.

   Suppose there are four right answers. Then the probability of picking one of them at random is 100%. But then there are no right answers. Contradiction.

   All possibilities lead to contradiction. There is no right answer.

2. 

   Samer Sabri August 25, 2012 at 5:57 am - Reply

   You are wrong. You didn’t check the case where it’s 0%.

   Proof: Assuming the probability is 0%, you have a 0% chance to get the right answer. He assumed the answer HAD to be in the answers.

   Rest of the proof: (prove 0 is the only answer) left as an exercice to the reader given the response above.

   • 

     Samer Sabri August 25, 2012 at 6:03 am - Reply

     By the way, just to be perfectly honest thought of this independently, saw the link through reddit but I only looked after I wrote the comment above

3. 

   Dave August 31, 2012 at 10:40 am - Reply

   Ok. So if you were to just pick randomly, you’d have a 1/4 chance, or 25%. But since there are two (seemingly) correct answers (that is, two choices that have 25% as an answer), then your odds are now 50%. BUT, 50% is one of the choices as well… which is only 1 of the 4 options… so that takes you back down to a 25% of getting the answer right. But, to me, that logic seems broken. I’m leaning towards the fact that there actually isn’t a correct answer because the question itself is “wrong” – that is, it can’t be solved. It feels like the answer is somehow recursive.

4. 

   MURIEL September 7, 2012 at 9:59 am - Reply

   50%

5. 

   Hope October 25, 2012 at 2:39 pm - Reply

   I agree with Dave!

6. 

   Paulo April 4, 2013 at 4:40 pm - Reply

   75%.
   Two answers are the same, 25-25, which means 50 %. If we consider there’s another answer corresponding to 50%, then 3 of them are correct.

7. 

   paula April 21, 2013 at 11:22 pm - Reply

   well i say it’s always 50% your answer is either right or wrong……50/50……

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