Growing Triangle - Growing Pain

This was both a fun and challenging puzzle that I have been playing with during the course of this week. Growing Triangle is the design of Andreas Rover, the man behind Burr Tools, a free software programme that has brought relief to thousands of frustrated puzzlers (myself included) and changed the course of history for designing and solving burr (and other) puzzle designs.

I obtained Growing Triangle from Andreas during the Puzzle Exchange at IPP35 in Canada two years ago. In Andrea's own words....

"This puzzle is inspired by "London Squares" which was designed by Li Zhunyou and exchanged by James Kerley at IPP34. Although I very much enjoyed the puzzle I spotted some "usability problems" and I want to fix with this design"

Growing Triangle is precision laser cut from 6mm clear acrylic< Made by Mr Puzzle, it consist of 12 irregular shaped pieces. Each of the pieces are also etched with markings to indicate the number of triangular units within. The finishing touches include a nice red drawstring pouch.

There are 11 challenges to the puzzle, simplest being to take 2 of the 12 pieces and form an isosceles triangle of 4 units length per side. Then take 3 pieces and form a triangle of 5 units per side, 4 pieces to form triangle of 6 units per side until all 12 pieces are used to form the largest triangle of 14 units length per side. Each challenge offers a unique solution and as you would imagine, moving from 2 to 12 pieces becomes progressively harder and painful. I have shown just the first two solutions here as an illustration of what this puzzle is about.

The first several challenges are not difficult and it is rather obvious which pieces are needed for the solve. From my personal standpoint it becomes "exponentially" difficult once you go past 5 pieces. The instructions do not tell you which of the 2, 3, 4, 5 and so on... pieces to use. You need to figure this out for yourself! But it does not require any form of random selection...rather if you study the puzzle sizes from the beginning, from 2 to 3 to 4 unit lengths and beyond, you will realise there is a trick to finding the area size of the next required piece as your triangle enlarges (grows). 

So far I have grown my triangle to 11 units length per side using 9 of the 12 pieces. But I have since remained stuck at this level (but I am still trying).

Oh, and did I mention that you can use Burr Tools to solve all 11 challenges of the puzzle? :-)