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 computer solutions by Charlie)

I see that at least one of the solutions presented, while convex, were self intersecting, like a star. I'll have to go back to the drawing board.

 

Posted by Charlie on 2009-04-25 00:43:11