# Tune a podracer and choose the pilots by solving the podracer tuning equation

A long time ago, in a galaxy far, far away...

These are troublesome times: The Galactic Republic is gone, the Jedi were exterminated due to Order 66, Vader and Palpatine rule the galaxy with absolute power as an evil Empire. The Empire had built a Death Star, which was used to destroy Alderaan, but the Rebel Alliance managed to destroy it. However, this is not enough because The Empire Strikes Back and what we really need is The Return Of Jedi.

Here you are, in Tatooine. You are a podracer mechanic working for the Reborn Dragons, a podracing team that uses podracing as a way to raise funds to support the Rebel Alliance. There are three categories of podracing, according to the Engine Power Yield: the Beginners $$(Y=1)$$, the Moderate $$(Y=2)$$ and the Masters $$(Y=3)$$. You are still unsure about the category that you should choose to enroll for racing.

Your job is to tune a podracer in order to ensure a victory in the next race. You are new to the job, since the experienced mechanic was captured by the Galactic Empire and imprisoned. The Rebel Alliance even managed to send him messages encoded in crosswords, but this is not enough.

There are many variables in your podracer:

• Power Recovery: You can set this as Low $$(R=1)$$, Moderate $$(R=2)$$ or High $$(R=3)$$.

• Energy consumption: You can set this as Low $$(E=1)$$, Moderate $$(E=2)$$ or High $$(E=3)$$.

• Levitation field strength: You can set this as Low $$(L=1)$$, Moderate $$(L=2)$$ or High $$(L=3)$$.

• Engine Orbiter field strength: You can set this as Low $$(O=1)$$, Moderate $$(O=2)$$ or High $$(O=3)$$.

• Hull Strength: You can set this as Low $$(HS=1)$$, Moderate $$(HS=2)$$ or High $$(HS=3)$$.

• Specific Acceleration: You can set this as Low $$(SA=1)$$, Moderate $$(SA=2)$$ or High $$(SA=3)$$.

The best category may be deduced by minimising the quantity $$x = (Y - 2)^2 + (R - 2)^2 + (E - 2)^2 + (L - 2)^2 + (O - 2)^2 + (HS - 2)^2 + (SA - 2)^2$$.

You should also choose two pilots to enroll, and you have six candidates with the following attributes:

Pilot Skill Fear Reflexes Trust/confidence Training
P1 1 - Poor 1 - Fearless 1 - Slow 3 - High 1 - Rookie
P2 1 - Poor 3 - Fearful 2 - Moderate 2 - Moderate 3 - Veteran
P3 2 - Moderate 2 - Moderate 2 - Moderate 2 - Moderate 2 - Moderate
P4 3 - Elite 3 - Fearful 3 - Fast 1 - Low 3 - Veteran
P5 1 - Poor 3 - Fearful 1 - Slow 1 - Low 1 - Rookie
P6 2 - Moderate 2 - Moderate 1 - Slow 2 - Moderate 1 - Rookie

Considering that each pilot attribute has the same weight (but could be either positive or negative, i.e. weight either $$+1$$ or $$-1$$), who are the two best pilots to choose? How is the pilots fear and confidence? What is the best way to tune the podracer (please, list each attribute one-by-one)? What is the best category? Post an answer answering those questions.

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I feel like I'm missing something because the optimization seems rather straightforward.

Enter the competition with yield

Y=2

and parameters

R=E=L=O=HS=HA=2

because

these mininimize the quantity x by making each square be 0.

For the pilot, choose

Pilots 4 and 3

because they have

the greatest and second greatest total weighted attributes, with skill, reflexes, trust/confidence, training being the natural positives, and fear being negative. Actually, even if fear is a positive, the answer is the same.