Mystery of the Integers: Unraveling Prob90

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https://www.physics.harvard.edu/uploads/files/undergrad/probweek/prob90.pdf

https://www.physics.harvard.edu/uploads/files/undergrad/probweek/sol90.pdf

This is the puzzle I am trying to understand. Does anybody has any idea how the table on the top of the second page i being deducted?

Some integers are being added and some appear to be randomly substituted...
 
Mathematics news on Phys.org
The first two of these facts show that if player X receives an E-triplet on a given
turn, then player Y can ensure that X receives an E-triplet on every subsequent
turn. Therefore, X must always create a non-E-triplet, by the first of the three
facts.

Why is that?Shouldn't he try to create a non-E-triplet since this is the LP for Y?
 

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