a b c d e f g h i j  1  C E B F E A E B H A A E H D F G E G D C F E B A H H B B C F D A D G E D H D B C C E D E G C G C D F C C B F A A C D G C F B C B C C B H E C A C E B E B A D D G D E G B C H D E B C  2   3   4   5   6   7   8   9

Draw the following set of convex polygons with vertices in ascending and consecutive alphabetical order:
triangle, square, pentagon, hexagon, heptagon and octagon.

Each vertex sequence begins with an A with subsequent (and all) vertices being 3 squares apart as defined by a chess knight's "L" shaped move or the queen's diagonal or orthogonal move.

No polygon is to have a common vertex with another. Should this occur then one or the other is not part of the solution.

(In reply to re(2): computer solutions -- fixed by Charlie)

In compiling this I used the Drawing toolbar in Excel to create templates which I could move around and rotate.

What I did not take into account was the full range of polygons possible given my definition of moves.  All of my polygons had at least one axis of symmetry, as did those of Jyqm (we differed in our solutions by just one vertex, 7b/6c, on the pentagon.

I have mapped out Charlie's polygons as overlays to my spreadsheet, and I might say I have quite a mess!!   He has introduced a few which do have at least one symmetry but then there are some which have none.

Wonder how this would have been had I specified "polygons with at least one axis of symmetry"?

Posted by brianjn on 2009-04-25 04:32:29