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Back to the Wall (Posted on 2010-04-28) Difficulty: 3 of 5

No! Not a firing squad nor the need for a continuous line to cross all line segments just once!

To each vertex labeled A to L apply a different value from 1 to 12. Let V, W, X, Y and Z be the sums of their respective surrounding vertices.

Provide at least one example where V=W=X=Y=Z, or offer a reason why this, like the continuous line, is impossible.

See The Solution Submitted by brianjn    
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re: If rectangle sums only of counters... | Comment 12 of 17 |
(In reply to If rectangle sums only of counters... by ed bottemiller)

When my original interpretation was used, having some of the polygons be pentagons (albeit with one 180 angle each), the common sum could be anywhere from 25 through 32.

When each is taken to be only a strict rectangle, with only four vertices, the common sum could be anywhere from 23 through 29, except not 26.

  Posted by Charlie on 2010-04-30 03:21:39
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