If you’ve gone to the Pyramids page, you already know that it’s probably our favorite pack in the game.
It might still be even if not for this design – which is exactly alike but completely different from the rest. Before I throw some geeky stats at you, here’s a quiz for you from one of the levels in the game based on this design:
note: this should read Connect the two dots in the only way you can to solve the puzzle, but I’m too lazy to edit the image.
While you’re pondering that problem, here’s a bit of board design geometry. The first design in Pyramids looks like this:
The design is far from random – and it took a bit of luck finding it. It results in some really cool levels – but only because the geometry is so precise.
There are 3 sets of walls:
a central pyramid that is 4 steps high.
a set of 4 high steps in the top left corner.
a set of 4 high steps in the top right corner.
The top of the pyramid aligns with the bottom of the corner steps, while the edges of the pyramid overlap with the edges of the corner steps (as demonstrated by the blue rectangle).
All four of the sectors are connected via shadow tiles as a result of the overlap. It’s a very unique wall pattern even for this game – and probably the most intricate.
Levels 1-30 in Pyramids are based on this design (there is also a minor variation, where the central pyramid is shifted to add a bit of variety). You can also find the 5 step high version of this in levels 61-90 of pyramids.
Back to the quiz. The answer:
Great job if you found that solution!
Now let’s look at the geometry of the featured design:
Can you see the similarities to the first design in Pyramids? It’s based on the same pattern – except the “steps” are 3 times bigger, and each set of walls is only 2 steps high.
Oops, turns out this is the correct way to connect the purple dots:
Ever see anything like that in any other connect the dots game?
That one line crosses 11 shadow tiles and travels the equivalent of 200 squares to connect dots that are just 2 squares apart. Keep in mind a computer generated the level – we didn’t set that up, we just saw it during testing.
While that’s an extreme example, you will see a lot of crazy lines like that with this design.
Let’s go into the numbers:
- 73% of the shadow tiles are crossed (19.73 out of the 27) – which is the most of any design in the game by over 5% (the 2nd highest, by the way, is the first design in Pyramids).
- It has the most walls of any design relative to the size of the board – the “wall factor” is 1.63, meaning it has 63% more walls than a closed rectangular design without any shadows would.
- The average line length is 15.47 tiles – that’s not even counting the shadow tiles. That’s also the highest in the game by quite a bit.
- The average maximum shadows crossed by a single line is 7.03. So, when you’re playing this level, you’ll usually see at least one line that crosses shadow tiles 7 times. That’s also the most of any design in the game.
But while the numbers are cool, we didn’t pick this design because of the numbers. It was our favorite before we even calculated these crazy stats. The numbers help explain why we liked it – but most importantly, the levels are fun, challenging, and look really cool.
Here’s the complete solution to the original puzzle:
