Pablo and Nacho write together a succession of positive integers of 2006 terms, according to the following rules: Pablo begins, who in his first turn writes 1, and from then on, each one in his turn writes an integer positive that is greater than or equal to the last number that the opponent wrote and less than or equal to triple the last number that the opponent wrote. When the two of them have written the 2006 numbers, the sum S of the first 2005 numbers written (all except the last one) and the sum T of the 2006 numbers written. If S and T are co-cousins, Nacho wins. Otherwise, Pablo wins. Determine which of the two players has a winning strategy, describe the strategy and demonstrate that it is a winning one.
combinatoricsnumber theory