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Find the number of solutions to a + b + c = 30, where a, b, c are positive integers.

 Nov 9, 2019
 #1
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If a, b, or c = 0, then there is 15 reversable ordered pairs for any of the two other variables adding up to 30. 

( a, b ) = 30

( b, c ) = 30

( a, c ) = 30 

 

15 * 3 = 45. Since the ordered pairs are reversable between two variables, 45 * 2 = 90 

 

Similarly, if a, b, or c = 1, then there is 14 reversable ordered pairs for any of the two variables adding up to 29. 

14 * 3 * 2 = 84 

 

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I advise to continue on with this method.

 Nov 9, 2019
 #2
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+1

There are 379 positive integers that satisfy the equation. They begin like this:

 

a       b     c
28    1     1
27    2     1
26    3     1
25    4     1
24    5     1
3      2     25
2      3     25
1      4     25
2      2     26
1      3     26
1      2     27.........etc.
Total =379 triplets.

 Nov 9, 2019

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