Your Rational Mind's Optimum Age

Algebra Level pending

Let f ( x ) = A x 3 + W x 2 − x − H f(x)=Ax^3+Wx^2-x-H where A A is your Age, W W is your Weight, and H H is your Height--all integers. There exists a healthy (W)eight that makes you feel taller while maintaining your mind's rational nature. Or, find W W such that f ( x ) f(x) has a rational factor, and then completely factor f ( x ) f(x) . Determine at what (A)ge your mind operates at peak rationality, or when f ( x ) f(x) has three rational factors.

34 years old 64 years old 54 years old 44 years old

Frank Giordano by Frank Giordano , 57, USA

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2 solutions

Frank Giordano
Sep 23, 2016

this facebook video explains the Game of G-filtered Polycules for Cubics; leave a comment.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Michael Mendrin
Sep 23, 2016

I'm 66, so I must be past my peak rationality. This was a particularly hard problem.

This is the first time I've ever heard of a "cubic bagel"

1 Helpful 0 Interesting 0 Brilliant 0 Confused

i wrote it a few years ago, just now exposing it. i didn't know G-filtered Polycules would be so useful reverse engineering problems. it's my new favorite hobby !o!

Frank Giordano - 4 years, 8 months ago

how did you solve this problem ???

Frank Giordano - 4 years, 8 months ago

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With the help of a friend, Mr Brutus Forcia. Much of the time, I had a hard time making sure I understood the problem correctly----such as, for example, "is that in inches?" It slowly dawned in me that it was nearly impossible to factor that cubic at all! So, on a hunch, I restricted my searches to A = 64 A=64 , finally factorized the cubic, and picked 64 64 to see what happens, instead of first checking the other possible answers. I got lucky.

Michael Mendrin - 4 years, 8 months ago

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thanks !!!

Frank Giordano - 4 years, 8 months ago

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@Frank Giordano – After reading your solution, I wonder now if there's a connection with the elliptic curve ? There seems to be some similarities.

Michael Mendrin - 4 years, 8 months ago

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@Michael Mendrin – interesting, i'll take a gander. thanks !!!

Frank Giordano - 4 years, 8 months ago

get the latest version of "G-filtered Polycules" here: https://www.facebook.com/groups/factorthis/

Frank Giordano - 4 years, 7 months ago

Won't you reach the again at 81?

Saya Suka - 4 years, 7 months ago

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i hope lol

Frank Giordano - 4 years, 7 months ago

yes, at perfect square ages in our life our minds operate at peak rationality. we just have to get there lol

Frank Giordano - 1 year, 9 months ago

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