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Winning strategy for last digit

Source: Tournament of Towns, Fall 2002, Junior O Level, P4

May 15, 2014
combinatorics proposedcombinatorics

Problem Statement

20022002 cards with numbers 1,2,…,20021,2,\ldots ,2002 written on them are put on a table face up. Two players A,BA,B take turns to pick up a card until all are gone. AA goes first. The player who gets the last digit of the sum of his cards larger than his opponent wins. Who has a winning strategy and how should one play to win?
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