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Find the number of ways of writing the positive integer 9 as the sum of exactly 5 positive integers, where the order of addends does not matter. 5 + 1 + 1 + 1 + 1 and 1 + 5 + 1 + 1 + 1 are considered one way.

 Sep 17, 2021
 #1
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You need to work out a logical system

 

id say  1+1+1+1+5     that is the only one with 4 ones

then     1+1+1+(two that sum to 6 but neither can be 1)

then    1+1+(three that sum to 7 but not including an more ones)

etc

when you exhaust all the possible combinations that inclu....

 

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thinking about it is is preobably easier to go from the big end.

The biggest number you can have is 5  (there is only the one possible way)

 

Now look at all possibilities that include fours.

 

You just need to find a logical system to list them all so that none will get forgotten or duplicated.

 Sep 18, 2021

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