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Wikipedia :   Fair division   |   Entitlement

(2017-02-24)   Sperner's Lemma   (Emanuel Sperner, 1928)
The number of full-color simplices in a  Sperner triangulation  is odd.

Sperner's lemma  is the combinatorial equivalent of Brouwer's fixed-point theorem.

Rental Harmony:  Sperner's Lemma in Fair Division  by  Francis Edward Su.
American Mathematical Monthly,  106 (1999)  pp. 930-942.
 
To Divide the Rent, Start With a Triangle  by  Albert Sun (New-York Times, 2014-04-28)
 
Sperner's lemma defeats the rental harmony problem (15:34)  by  Burkard Polster  (Mathologer, 2017-02-10).
Splitting Rent with Triangles (16:20)  by  Kelsey Houston-Edwards (PBS Infinite Series, 2017-02-23).
Proving Brouwer's fixed-point theorem with Sperner's lemma (19:29)  by  Trefor Bazett (2018-03-11).
 
Wikipedia :   Sperner's lemma (1928)   |   Emanuel Sperner (1905-1980)

(2017-02-24)   Stolen Necklace Problem
With  N  different types of  beads,  N  cuts are enough for a fair split.

Borsuk-Ulam Theorem (21:54)  by  Grant Sanderson (3Blue1Brown, 2017-02-10).
Borsuk-Ulam Theorem (16:36)  by  Trefor Bazett (2018-12-16).
 
Wikipedia :   Borsuk-Ulam Theorem   |   Karol Borsuk (1905-1982)   |   Stanislaw Ulam (1909-1984)