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 Absolute Value Muse (Posted on 2014-02-19)
Determine the number of integer solutions to:
|x|+ |y| + |z| = 15

Note:

The absolute value function F(x) = |x| is defined as:
```        x if x ≥ 0
F(x) =
-x if x < 0
```

 No Solution Yet Submitted by K Sengupta Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): General Solution -- Two geometric methods Comment 4 of 4 |
(In reply to re: General Solution -- Two geometric methods by Charlie)

Well, Charlie, since you put it that way, this matches up to my second method.

C(n-1,2)*8 = number of integral points on side of the octahedron excluding edges = 4n^2 - 12n + 8

(C(n+2,2)-C(n-1,2)-3)*4 = number of integral points on edges of the octahedron excluding vertices = 12n - 12

6 = number of vertices on octahedron

So, as expected,  C(n-1,2)*8 + (C(n+2,2)-C(n-1,2)-3)*4 + 6 = 4*n^2 + 2

 Posted by Steve Herman on 2014-02-20 19:44:28

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