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Obduction puzzle guide: Solve puzzles, count like an alien and learn base 4

Jeffrey Parkin (he/him) has been writing video game guides for Polygon for almost seven years. He has learned to love just about every genre of game that exists.

In Obduction, the Villeins use a base 4 number system — and you'll have to use it to solve puzzles. To understand it, you have to think about our own numbers for a minute.

Our numbers

We use base 10. This means that every digit, reading from right to left, represents a count of exponentially increasing factors of 10 starting on the right with 10^0. (Any number to the zeroth power is one.) The next digit to the left is 10 to the first power, followed by 10 to the second power, etc. This is called positional notation.

Broken down this way, you can write the number 3 as 3 x 10^0.

Multiple digits use the same math and then get added together. You can read the above example as 3 * 10^0 + 2 * 10^1 + 1 * 10^2.

Their numbers

In base 4, you just replace the exponents of 10 with exponents of four. Therefore, you can write the number three as 3 x 4^0.

This gets more complicated when there are multiple digits — any number greater than three — but the math stays the same.

Counting connections

Villeins frustratingly don't use Arabic numerals like we do. While it looks confusing, the Villein system is actually quite simple. Just count the number of connections to the central dot and multiply like in the image below. Technically, this means the lines between dots could go in any direction, but the Villein standard uses specific connections.

The same logic applies to larger numbers. For our example of 27 above, it can be read as 3 connections * 4^0 + 2 connections * 4^1 + 1 connection * 4^2.

The next difference is that Villein numbers aren't written out in columns like ours. They are arranged in a grid.

The increasing number positions are arranged in a spiral.

So our example of 27 from earlier looks like this.

To pick a more useful example, the number 406 looks like this. In base 4, this can be read as 2 x 4^0 + 1 x 4^1 + 1 * 4^2 + 2 * 4^3 + 1 x 4^4.

Obduction guide full table of contents

Navigating Obduction (and our guide)

We've organized our Obduction guide based on worlds and what you do in them, so each section is a world, and chapter's name represents a puzzle or an objective. Every page flows into the next, and you can use the quick navigation box just above to hop to the previous or next area.

In long chapters, there's a table of contents at the top of the page. In every chapter, there's a table of contents at the bottom showing Obduction in its entirety. If you're not sure exactly where to go, just look at the copious images on each page. When they look familiar, you'll be able to orient yourself.