Unsolvable problem - but the teacher says it is - help

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smarshall007

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Oct 11, 2022
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Hello All,

The problem is as follows:

The sum of two consecutive odd numbers less 12 is 58.

I have had 3 people look at it. One includes a retired math professor. Help
 
smarshall007 said:
Hello All,

The problem is as follows:

The sum of two consecutive odd numbers less 12 is 58.

I have had 3 people look at it. One includes a retired math professor. Help
Click to expand...
As the problem is written by you, according my interpretation, I agree with your stated result.

How have YOU tried to solve it? Please share your work - so that the interpretations can be validated.
 
smarshall007 said:
Hello All,

The problem is as follows:

The sum of two consecutive odd numbers less 12 is 58.

I have had 3 people look at it. One includes a retired math professor. Help
Click to expand...
Technically, that isn't a problem! It's just a statement.

The problem presumably asks you to find the two numbers.

Now work through it very slowly. I think you are confusing "consecutive odd numbers" with "consecutive numbers", They are not the same thing, but it's easy to overlook. (I did at first!)
 
You never said what the 3 people who look at it said.

The problem is very solvable. What should the total of the two number be?
 
As Dr. Peterson said, you have not even told us what the problem is. All that you have told us is that three people, one a retired teacher and two unspecified, assert the unknown problem to be insoluble and a fourth person, also a teacher, assert the unknown problem is soluble.

There is a reason that we ask for the exact and complete text of the original problem.

If the problem is

Are there two consecutive odd integers such that the difference between their sum and 12 equals 58

then the problem is quite soluble. The answer is NO.

But some other problem may not be soluble. How do we know if you do not give us the actual words of the problem?
 
Given [imath]n[/imath] is odd, the next consecutive odd number is [imath]n+2[/imath]. The problem states that there is some value for [imath]n[/imath] where the following is true:

[imath]n + (n + 2) - 12 = 58[/imath]​

The problem is apparently asking what are the values of the odd numbers that satisfy the equation. However, the solution for [imath]n[/imath] here is an even number. If that is indeed what the teacher meant, then the problem is unsolvable.
 
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