Node Investigation Notes

(1) The minimum Node Total is given by joining all the matches in a ring or line.

If the number of matches is n then the minimum total is 2n.

(2) The maximum Node Totals can be created by adding onto the maximum pattern for 3 matches;

The pattern will always contain an obtuse angle into which another match can fit to give two new 3 nodes so hat the total is increased by 6.

If the number of matches is n then the maximum node Total is 6(n – 1)

Practically it becomes increasingly difficult to create the new patterns.

(3) 4 matches and no loose ends gives totals of 8 and 12 (not 10)

5 matches give totals of

10 12 14 16 18

(4) If n is the number of matches then the maximum Node Total is 6(n-2) for patterns with no loose ends.