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February 9th, 2007, 12:55 PM  #1 
Senior Member Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0  Mistakes occur at all levels. ;)
"On a rafting trip, when nothing exciting was happening, the four of us each picked a nonprime positive integer. The greatest common factor of each pair of integers was 1. What is the least possible sum of our four integers? (Recall that 1 is not prime.)" The above problem is taken from a math contest, and there is a significant mistake in the wording. The 'correct' answer is not the most valid interpretation of the question as written. 1) Correctly interpreting this question will give a different answer from the answer that the test writer was looking for. What are these answers and what is the difference in interpretation? 2) How could the wording be changed so that the intended interpretation is the only possible one? 3) Given the intent of the author and the way the question is actually worded, what answer(s) would you consider to be correct. 
February 10th, 2007, 08:53 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,937 Thanks: 2210  Re: Mistakes occur at all levels. ;)
1) There are various ambiguities, but I assume that what you're referring to is the possibility that all four chose the number 1. I am not prepared to go further, in the light of other ambiguities. 2) The particular issue mentioned above could have been dealt with by stating that only one of the four chose the number 1. The question would still have needed to be reworded to avoid other ambiguities. 3) The question is ambiguous, so "it depends". Beyond that, an ambiguous question doesn't have any valid answers. I can think of less exciting activities than rafting or choosing numbers for the above type of question, such as walking slowly round a square. 
February 10th, 2007, 01:34 PM  #3 
Senior Member Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 
The above question was from the Ohio Math League (and presumably from math leagues in other states, as well). They decided to simply throw the question out and simply give everyone who participated the point for the question. To what other ambiguities were you referring, skipjack? I'm not finding any. 
February 12th, 2007, 12:35 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,937 Thanks: 2210 
There is poor wording in the question, in that the activity of each person choosing an integer is evidently more exciting than rafting, since they chose to do it. Also, it isn't stated that they chose at random from some population, so the sum doesn't vary by implication over a random process. If the sum is 11, say, there is no alternative  that is what the numbers happened to add up to. However, the ambiguities I was referring to are those in the numbered questions, not the original scenario. Those questions contain various illdefined terms. 
February 12th, 2007, 03:09 PM  #5 
Senior Member Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 
Apparently, I'm not up to the task of unambiguously discussing ambiguities. 

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