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Xech is a shiny new robot on it’s first day of work. Xech's job is to move packages and product around a warehouse that is used by Xechry merchants, keep things neat, tidy, and efficient. At 9:00am sharp Xech gets its first set of instructions to fetch a package from the warehouse. The instructions are as follows:

Proceed to the charging station and face South.

Move forward 35 yards and then turn 270 degrees counterclockwise.

Move backwards 15 yards and then turn 45 degrees clockwise.

Move forward 5 yards, reverse your direction and move forwards another 40 yards.

Turn 135 degrees anti-clockwise and move forward 90 yards.

Rotate 45 degrees to the robots left and move forward 15 yards.

Raise your robot arms 2 feet and grab the package in front of you

Spin around 180 degrees and move forward 2 feet

Turn 90 degrees to your left and move forward until you see the dotted line on the floor.

After performing these instructions, In which direction will Xech be facing?

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    $\begingroup$ Welcome to Puzzling! This seems like a pure mathematics question, with no actual puzzle content - is there something else going on? $\endgroup$
    – Deusovi ♦
    Commented Feb 11, 2020 at 16:51

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Just to elaborate on Ryan Huber's answer, to get the final direction the robot faces we can

Ignore all the distance instructions and just focus on the instructions where the robot changes direction.

Procedure

"face South" $\rightarrow$ S
"turn 270 degrees counterclockwise" $\rightarrow$ W
"turn 45 degrees clockwise." $\rightarrow$ NW
"reverse your direction" $\rightarrow$ SE
"Turn 135 degrees anti-clockwise" $\rightarrow$ N
"Rotate 45 degrees to the robots left" $\rightarrow$ NW
"Spin around 180 degrees " $\rightarrow$ SE
"Turn 90 degrees to your left" $\rightarrow$ NE

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    $\begingroup$ What if the factory is at the south pole? $\endgroup$
    – Sneftel
    Commented Feb 11, 2020 at 16:18
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    $\begingroup$ @Sneftel Indeed, if the charging station is at the South Pole, then the robot will fail at the first step. I have ignored uncommon starting points here because it is not clued in the puzzle and because there are many different possible outcomes. $\endgroup$
    – hexomino
    Commented Feb 11, 2020 at 16:31
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    $\begingroup$ Just being pedantic. :-) To judge from the body of questions on this site, though, the vast majority of people and things which go in a particular direction are apparently located at the north or south pole. ;-) $\endgroup$
    – Sneftel
    Commented Feb 11, 2020 at 16:33
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Xech will be facing North-East, with a heading of 45 degrees.

Facing South at the beginning. Turns 270 degrees, now facing West. Turns 45 degrees, now facing North-West. Turns around, now facing South-East. Turns 135 degrees, now facing North. Turns 45 degrees, now facing North-West. Turns 180 degrees, now facing South-East. Turns 90 degrees, now facing North-East. Final position, facing North-East.

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  • $\begingroup$ would you like to elaborate on your answer? $\endgroup$
    – Prince North Læraðr
    Commented Feb 11, 2020 at 16:06

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