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 A Tri Star Issue (Posted on 2008-06-01)
The letters, A to L, within this star represent intersections of unique pairings of its 6 lines, and α, β, γ, δ, ε and ζ are sums of intersections defined as:
```α = A + D + G + K     β = E + G + J + L    γ = K + J + I + H
δ = L + I + F + B     ε = H + F + C + A    ζ = B + C + D + E
```
```
A α
/ \
ζ  B---C---D---E  β
\ /     \ /
F       G
/ \     / \
ε  H---I---J---K  γ
\ /
L  δ

```
Assign values from 1 to 12 to each of the locations A to L such that each sum is an element of an arithmetic progression with an arithmetic difference of two (2) but not necessarily as adjacent vertex values.

Secondly, attempt the same task but with a difference of four (4) as the outcome.

And for a tease... can you offer a solution if all such vertex sums are equal, ie, 26?

Note:
Discounting rotations and reflections, more than one possibility exists for each of the first two tasks.

 See The Solution Submitted by brianjn Rating: 4.0000 (2 votes)

Comments: ( You must be logged in to post comments.)
 Subject Author Date re: Can we prove? - I can pcbouhid 2008-06-03 22:00:08 Can we prove? pcbouhid 2008-06-03 14:51:29 Might as well diagram the 94 difference-4, adjacent-vertex solutions. Charlie 2008-06-02 22:29:47 So Many brianjn 2008-06-02 22:14:19 re: Some thoughts (without reading Charlie´s comments) brianjn 2008-06-02 20:46:16 re(2): A method to find solutions for the tease - need improvement - one step ahead pcbouhid 2008-06-02 19:10:00 re: A method to find solutions for the tease - need improvement pcbouhid 2008-06-02 14:10:30 A method to find solutions for the tease pcbouhid 2008-06-02 12:03:21 The final "tease" solutions; worked out correctly this time, I hope. Charlie 2008-06-02 09:49:16 Some thoughts (without reading Charlie´s comments) pcbouhid 2008-06-02 09:30:49 re(2): computer solution; spoiler Charlie 2008-06-02 00:24:25 re: computer solution; spoiler Charlie 2008-06-02 00:06:57 computer solution; spoiler Charlie 2008-06-01 23:56:16 Stupid! Stupid! Stupid!! brianjn 2008-06-01 22:32:06 re: Possible mistake? brianjn 2008-06-01 21:59:36 re: Possible mistake? Charlie 2008-06-01 13:22:39 Possible mistake? pcbouhid 2008-06-01 12:39:22
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