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In how many ways can 27 be written as the sum of two positive integers?  (Ignore the order of the numbers.)

 May 26, 2020
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By positive...

 

In some places 0 is considered positive and negative, some neither.

 

I'll go with the assumption 0 is neither since where I live that's the definition.

 

Thus we have the pairs...

 

 1 26

2 25

3 24

 

...

 

26 1

 

1 through 26 is 26, so we have 26 pairs. There are 13 distinct pairs and times 2 for the ability to flip over. This is because 27 is odd and 27/2 isn't an integer.

 

If the number was odd however we would have a pair (even num.)/2 and we can't flip that.

 

If you don't understand anything feel free to ask!

 

(sorry for the late answer!)

 May 26, 2020

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