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I'm pursuing an Artificial Intelligence course online and I don't understand how the state space is calculated. In the following PDF on page 3 slide 2 it says that the possible pacman positions are:

12x10 = 120

Why is it so? And how did we get to this number?

Actually this is an excerpt from an online course by UC Berkley on Edx and though it is not shown in this slide but while calculating the state space they do the following:

12 x 10 x 4

where 4 is for the four directions in which the pacman can face, also it was never told that the area is bigger or they are only showing a portion o it.

anonn023432
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    Probably means that there's 6 rows, 5 columns, and Pacman can be looking at 4 directions. So there you go 120 different positions. – Dleep Sep 23 '15 at 20:02
  • Edit: There was a previous answer which was deleted for some reason which said that the pacman on that image was too small compared to the other ones, so there are probably 12 rows and 10 columns in there. That's probably the right answer. After all it makes no sense for a pacman to move BETWEEN food dots. – Dleep Sep 23 '15 at 20:04
  • The orientation is not part of the state as Pacman can move to every direction without having to turn first. It's just a visual gimmick but not important for planning. – FooTheBar Sep 23 '15 at 20:06
  • I think @Dogbert is correct and the pacman can move in both the empty columns and rows and the columns and rows with the food pellets – anonn023432 Sep 23 '15 at 20:20

1 Answers1

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This is because there are:

  • 10 columns: five with "pellets" in them, and five that are empty.
  • 12 rows: six with "pellets" in them, and six that are empty.

enter image description here

Cloud
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  • Oh, this seems to be the likely answer. I assumed that the pacman would only move on the columns and rows with the food pellets and it was shown this way so that we can easily count the number of food pellets – anonn023432 Sep 23 '15 at 20:18