As you place more pieces you have less freedom to place the next piece because you have fewer pieces in hand to choose from. So one needs to find a strategy that maximises the freedom to move at the later stages. More exactly, it's easy to check the solution once it's proposed. Otherwise the number of possible candidate solutions for a general tiling problem with 209 pieces is almost as large as the total number of conceivable ways of combining 209 objects. And there might be no specially intelligent way of cutting down that search space.
Squares are easy, everyone can do equilateral triangles or regular hexagons.
After that much, this is a big subject called tesselation about which whole books are written. The worst case is pretty bad, and if one could solve it in reasonable amounts of computer time, for whatever types of pieces to tile together, that would unexpectedly solve many other problems. And then there's some interesting middle ground. You could say that's why Eternity was intriguing. In June 1999 the puzzle was launched and my brother Matthew bought me a copy, for my birthday.