As I was searching for something on google, I saw an ad at the bottom of the page. The ad was about the Davinci code new movie that is coming out. I clicked and found a sudoku like puzzle, related to the movie. The puzzle is explained in the following two pictures (description can also be found on:

Well… it is clearly a very simple problem for a constraint solver, like Alloy Analyzer! I created the following model (took me half an hour, so no comments or too much thought about it).

Alloy Analyzer came up with a solution in 3 seconds, on the dual core 2GB RAM opteron server running linux!

The solution is the following one:

symbol= { (Cell_0 Blade_0) (Cell_1 Blade_0) (Cell_2 Blade_0) (Cell_3 Blade_0) (Cell_4 Fi_0) (Cell_5 Fi_0) (Cell_6 Fi_0) (Cell_7 Fi_0) (Cell_8 Cross_0) (Cell_9 Cross_0) (Cell_10 Cross_0) (Cell_11 Cross_0) (Cell_12 Star_0) (Cell_13 Star_0) (Cell_14 Star_0) (Cell_15 Star_0) }

rowIndex = { (Cell_0 One_0) (Cell_1 Two_0) (Cell_2 Three_0) (Cell_3 Four_0) (Cell_4 One_0) (Cell_5 Two_0) (Cell_6 Three_0) (Cell_7 Four_0) (Cell_8 One_0) (Cell_9 Two_0) (Cell_10 Three_0) (Cell_11 Four_0) (Cell_12 One_0) (Cell_13 Two_0) (Cell_14 Three_0) (Cell_15 Four_0) }

columnIndex = { (Cell_0 One_0) (Cell_1 Four_0) (Cell_2 Three_0) (Cell_3 Two_0) (Cell_4 Four_0) (Cell_5 Three_0) (Cell_6 Two_0) (Cell_7 One_0) (Cell_8 Three_0) (Cell_9 Two_0) (Cell_10 One_0) (Cell_11 Four_0) (Cell_12 Two_0) (Cell_13 One_0) (Cell_14 Four_0) (Cell_15 Three_0) }

It is quite straightforward! The symbol of Cell_0 is Blade, its row is One and column One. The symbol of Cell_1 is Blade again, he row is Two and Column Four etc.

The symbol names are not related to the movie or book symbol names. In my model Blade is the pyramid like shape, Fi is the Greek letter fi, Cross is the symbol that looks like a cross and Star is the symbol that looks like a star. I know that I spent half an hour to solve a problem that would have taken me around 10 minutes to solve manually, but as a proper nerd I prefer to use my (few) grey cells to think how to use a computer to solve a problem for me, instead of solving the problem myself.

Well.. that’s it! I don’t want to spend more than 1 hour on this!

There are a couple of blogs with solutions to the puzzles.
Links to solutions:

UPDATE: I used the model on my P4 running @ 2.8G with 712 MB ram and took AA 23 seconds to solve the problem. Not bad at all! But for bigger problems the state space will be increased by too much. Looks like an AI technique should be used to find a solution.

3 thoughts on “Using Alloy Analyzer to solve the first Google Davinci Code Quest puzzle!

  1. You have kindled my curiosity in Alloy. The version of Alloy I studied 2 years back was 1.0 but the Alloy code you posted here seemed to be very different. By any chance, can you tell me which Alloy version you used.

  2. Hi James,

    I used Alloy v3.0 (the one that is available from the alloy website) for the model. It is very easy and quick to develop models and check properties of (especially static) systems with the latest version of the language.

  3. or a quantum computer… here is a phd topic if you want to do another one: quantum complexity bounds in the quest for cracking the generalised da vinci code. hmmm… lovely!


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