The earliest that the Kahlo could be auctioned is

Irina on January 7, 2020

@sprozes,

This is a linear game that requires us to determine the order of six paintings - J K N R S V.

___ ___ ___ ___ ___ ___

The following rules apply:

(1) J cannot be auctioned immediately before or after V.
This rule tells us that we cannot have JV or VJ combination.
~ (VJ v JV)

(2) V must be auctioned off earlier than K, and K must be auctioned earlier than S
This rule tells us that we have the following chain, meaning that S cannot be auctioned first or second, K cannot be auctioned first or sixth, and V cannot be auctioned fifth or sixth:

V < K< S


___ ___ ___ ___ ___ ___
1 2 3 4 5 6
~S ~S ~V ~V
~K ~K


(3) N must be auctioned second or third.
/N /N
___ ___ ___ ___ ___ ___
1 2 3 4 5 6
~S ~S ~V ~V
~K ~K

(4) R must be auctioned earlier than N.

R>N

Since N must be auctioned second or third, we can conclude that R must be first or second.

/R R/N /N
___ ___ ___ ___ ___ ___
1 2 3 4 5 6
~S ~S ~V ~V
~K ~K

Considering how restrictive these two rules are, this game can be reduced to three base scenarios:

(1) R N V K J/S S/J
(2) R __ N __ __ __
(a) R V N __ __ __ K/S/J are free variables and could go in any order as long as K (b) R J N V K S
(3) __ R N __ __ __
(a) V R N __ __ __ K/S/J are free variables and could go in any order as long as K < S
(b) J R N V K S

With this in mind, let's look at the questions. The question asks us when is the earliest K could be auctioned off. By looking at the scenarios above, we can see that the earliest K could be is 4th because the first three slots are always taken by a combination of V/J R N (D).

Let me know if this makes sense and if you have any other questions.