"Circular Payments - Equalization of Debts" Problem

mgbvox

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Oct 24, 2016
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I recently put on a cabaret show after which myself (Matt) and two other parties (James and Christine) covered expenses (for room rental, handling sales, etc...) in an uneven manner; therefore, I (Matt) am "in the hole" $M while Christine is in the hole $C, and James is in the hole $J. I would like to set up a payment scheme so that I pay Christine $A, Christine pays James $B, and James pays me $C, such that we all wind up with the same amount of money and our debts "equalize;" i.e. M - A + C = C - B + A = J - C + B. A visualization of the cycle:
attachment.php

This seems like a fairly straightforward problem, but I'm blanking on how to start. Any help would be appreciated!
 

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I recently put on a cabaret show after which myself (Matt) and two other parties (James and Christine) covered expenses (for room rental, handling sales, etc...) in an uneven manner; therefore, I (Matt) am "in the hole" $M while Christine is in the hole $C, and James is in the hole $J. I would like to set up a payment scheme so that I pay Christine $A, Christine pays James $B, and James pays me $C, such that we all wind up with the same amount of money and our debts "equalize;" i.e. M - A + C = C - B + A = J - C + B....
How are you defining "in the hole", such that all parties are "in the hole" (being shorted), with nobody being "to the good" (having an overage)? Thank you! ;)
 
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