Sandcastle Builder - Glass Ceilings Again

Somehow it turns out that playing well actually helps in Sandcastle Builder. I mean, botting helps a lot too, but I was pretty amazed that I had Logicat before I got to the long pix. I knew the different phases of the game so I didn't have to do things I did the first time like spend a day figuring out that I was now progressing exclusively through Blast Furnace.

I'm still a ways from infinite sand but I am definitely in the part of the game where I regard the amount of sand I have as an order of magnitude rather than as an ordinary number. I'm generally looking to "lose" a the Monty Haul Problem because multiplying my castled by one and a half is basically nothing and losing them all hardly matters.

As any Sandcastle Builder player knows, part of reaching the ten-to-the-thirty-plus castles phase of the game is breaking the glass ceiling.

If you are unfamiliar, glass ceilings are boosts that multiply the return of your tools by 33 per glass ceiling you have. For example, glass ceiling 0 affects buckets, so if you have it your buckets produce 33 times as much. Glass ceiling 1 affects bots, so if you have both ceiling 0 and ceiling 1 both your buckets and bots produce 1089 times as much. There is a ceiling for each tool, so having all the ceilings up the rivers - ten in all - multiplies all of those tools production by 1.5×10¹⁵ which really is quite a lot.

But purchasing the glass ceilings is complicated. You can always buy glass ceiling 0 once it is unlocked by earning logic levels. You can buy any other glass ceiling if you have the glass ceiling immediately before it but no others before it. For instance, you can buy glass ceiling 3 if you have glass ceiling 2 but not ceilings 0 or 1. Of course to meet that condition you have to lock glass ceilings you already have. You can lock a glass ceiling under the same condition you can buy it - if you have ceiling immediately before it but no others before it.

How does this work in practice? To get ceiling 1 you have to buy 0. To get ceiling 2 you need to lock 0. To get ceiling 3 you'll need to lock 1 but to do that you have to buy 0 so you buy it and then lock 1 and then lock 0. Now you want ceiling 4 so you buy 0, buy 1, lock 0, lock 2, buy 0, lock 1, lock 0 leaving you with just 3 so you can buy 4. Then to get 5 you buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, lock 3, buy 0, buy 1, lock 0, lock 2, buy 0, lock 1, lock 0, buy 5.

It was 1 click to buy 0, 1 click to buy 1, 2 clicks to buy 2, 4 clicks to buy 3, 8 clicks to buy 4 and 16 clicks to buy 5. Yes, when you have just purchased ceiling 8 you are looking at 256 more clicks to buy ceiling 9 after which you have just 8 and 9 so you have to buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, buy 3, buy 0, buy 1, lock 0, lock 2, buy 0, lock 1, lock 0, buy 4, buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, lock 3, buy 0, buy 1, lock 0, lock 2, buy 0, lock 1, lock 0, buy 5, buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, buy 3, buy 0, buy 1, lock 0, lock 2, buy 0 , lock 1, lock 0, lock 4, buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, lock 3, buy 0, buy 1, lock 0, lock 2, buy 0, lock 1, lock 0, buy 6, buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, buy 3, buy 0, buy 1, lock 0, lock 2, buy 0, lock 1, lock 0, buy 4, buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, lock 3, buy 0, buy 1, lock 0, lock 2, buy 0, lock 1, lock 0, lock 5, buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, buy 3, buy 0, buy 1, lock 0, lock 2, buy 0 , lock 1, lock 0, lock 4, buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, lock 3, buy 0, buy 1, lock 0, lock 2, buy 0, lock 1, lock 0, buy 7, buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, buy 3, buy 0, buy 1, lock 0, lock 2, buy 0, lock 1, lock 0, buy 4, buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, lock 3, buy 0, buy 1, lock 0, lock 2, buy 0, lock 1, lock 0, buy 5, buy 0, buy 1, lock 0, buy 2, buy 0, lock 1, lock 0, buy 3, buy 0, buy 1. That's just another 170 clicks for a total of 682 clicks if you don't make any mistakes.

I made a few mistakes.

Image by Ævar Arnfjörð Bjarmason CC-licenced

Those with a mathematical bent will notice this problem is extremely similar to the Towers of Hanoi - imagine locked ceilings are in the starting tower, unlocked ceilings are the tower you want to get them to and the store is middle tower but because of some minor differences it takes fewer moves. The similarity to Towers of Hanoi, though, actually means the game is super simple - especially because the set-up prevents the wrong moves. All you have to do is keep making legal moves without ever taking back a move and you win.

Look at the sequence above, with no ceilings the only think you can do is buy 0, then the only thing you can do is buy 1, then the only thing you can do is lock 0, etc. There are never any choices to make, you just have to remember which direction you are headed in. Over the long course of the process that's not quite as easy as it sounds, especially if you are distracted by a baby, but it's certainly not hard to succeed and obviously you'll realize you headed in the wrong direction soon enough.

When you have glass ceilings 0 through 9 you get an achievement that makes it so in the future glass ceilings are unlocked by the DoRD so you don't need to do this again when you Molpy Down. I had to do it a second time because I was starting an entirely new game.

If this sounds like the worst game ever then you are just a very different person than me. I thought this was going to be awful and tedious to do a second time but instead I found it really engaging. There is a very good reason I named this my second favourite game of 2013.

So now that I have broken the glass ceiling and hit the long pix I was able to upgrade Factory Automation to 11. Now I just need to bust open a bunch of crates to get the glass blocks to start blackprint work.

If you don't know what any of that means, you have to admit, it sounds awesome!