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A Tri Star Issue (Posted on 2008-06-01) Difficulty: 3 of 5
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 canpcbouhid2008-06-03 22:00:08
QuestionCan we prove?pcbouhid2008-06-03 14:51:29
SolutionMight as well diagram the 94 difference-4, adjacent-vertex solutions.Charlie2008-06-02 22:29:47
So Manybrianjn2008-06-02 22:14:19
re: Some thoughts (without reading Charlie´s comments)brianjn2008-06-02 20:46:16
re(2): A method to find solutions for the tease - need improvement - one step aheadpcbouhid2008-06-02 19:10:00
re: A method to find solutions for the tease - need improvementpcbouhid2008-06-02 14:10:30
A method to find solutions for the teasepcbouhid2008-06-02 12:03:21
SolutionThe final "tease" solutions; worked out correctly this time, I hope.Charlie2008-06-02 09:49:16
Some ThoughtsSome thoughts (without reading Charlie´s comments)pcbouhid2008-06-02 09:30:49
re(2): computer solution; spoilerCharlie2008-06-02 00:24:25
Solutionre: computer solution; spoilerCharlie2008-06-02 00:06:57
Solutioncomputer solution; spoilerCharlie2008-06-01 23:56:16
Stupid! Stupid! Stupid!!brianjn2008-06-01 22:32:06
re: Possible mistake?brianjn2008-06-01 21:59:36
re: Possible mistake?Charlie2008-06-01 13:22:39
QuestionPossible mistake?pcbouhid2008-06-01 12:39:22
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