MatheStatica

I am the very model of a self-recursive modeler

I am the very model of a self-recursive modeler
My consciousness encompasses itself in many meta layers


To Russel’s paradox, I have the set of all the answers
I cut the hair of all the non-self-barbering hairdressers


I think about me thinking of my thoughts with regularity
In my Cartesian theater, I see myself with clarity


I tell you that I lie without the slightest contradiction
The story of my life is told in meta-metafiction


My inner simulator replicates the total universe
I simulate myself as I am writing out this line of verse


My secrets are unknown to me, I keep them confidential
Referring to myself I’d say I’m quite self-referential


My strange loop’s Escherer than yours, it’s Bacher and it’s Godeler
I am the very model of a self-recursive modeler

Poem by: Jacob Falkovich (https://putanumonit.com/2018/08/28/very-model/)

I am the very model of a self-recursive modeler I am the very model of a self-recursive modeler My consciousness encompasses itself in many meta layers

Complete leaderboard till Week #4.

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Week #1 Problem

While searching his father’s attic, Hugo finds a solid cube circumscribed by a sphere. A note accompanying the same poses an interesting challenge. Hugo has to cut the cube into a finite number of rectangular parallelepipeds and use smaller spheres to circumscribe them, in such a way that the volume of the circumscribed sphere of the cube is equal to the sum of the volumes of all spheres circumscribed to the parallelepipeds.

Show that the only possible way for Hugo to achieve the target is to cut the cube into smaller cubes.

Answers to be taken through email only. (Deadline: 5th August'18)