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what is the smallest number that can be written as a sum of three natural numbers in two different ways?

 Mar 21, 2022
 #1
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the answer is 251

 Mar 21, 2022
 #2
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what is the smallest number that can be written as a sum of three natural numbers in two different ways?

 

How about 11.  (1 + 3 + 7) and (2 + 4 + 5)   I can't swear that 11 is the smallest but it's smaller than 251.  

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 Mar 21, 2022
 #3
avatar+23183 
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8  =  4 + 3 + 1

8  =  5 + 2 +1

 Mar 21, 2022
 #4
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Hi Geno, That's a good one, and I did think of it.  I didn't submit it because,  

although the problem isn't explicit about not using the same number in both  

groups (i.e., the "1"), I imposed that limitation on myself. 

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Guest Mar 22, 2022

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