MathDB

Nina and Tadashi play the following game. Initially, a triple

(a, b, c)

of nonnegative integers with

a+b+c=2021

is written on a blackboard. Nina and Tadashi then take moves in turn, with Nina first. A player making a move chooses a positive integer

k

and one of the three entries on the board; then the player increases the chosen entry by

k

and decreases the other two entries by

k

. A player loses if, on their turn, some entry on the board becomes negative.
Find the number of initial triples

(a, b, c)

for which Tadashi has a winning strategy.

Problem Statement