Xiaoming's winning strategy is to ensure that one odd number is erased at a time (if the odd number has been erased, it will be erased).
Xiao Cong's winning strategy is to ensure that the number of erasers each time is in the same group as that of Xiao Ming (see below for the grouping method).
(Because the number erased randomly by the referee is written on the blackboard, both Xiao Cong and Xiao Mingcan have seen it-even if they don't know what the number is, they should adopt this strategy. )
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Reason:
In 2008, there were 1003 odd numbers and 1004 even numbers (* * 2007 positive integer).
If the number erased by the referee is odd:
Xiao Ming only needs to make sure to erase one odd number at a time (but if the odd number has been erased, he can erase it at will).
In the end, there must be two even numbers left, and Xiao Ming wins;
If the number erased by the referee is even (recorded as 2K):
According to the method that the number less than 2K is 2X, 2X+ 1, and the number greater than 2K is 2Y- 1, 2Y, the remaining numbers are divided into 1002 groups every two.
As long as Xiao Cong guarantees that the number of erases each time is in the same group as that of Xiao Ming, there will inevitably be two adjacent positive integers left in the end, and Xiao Cong wins;
Numbers less than 2K are the same group 2X, 2X+ 1, and numbers greater than 2K are the same group 2Y- 1, 2Y, namely:
2, 3, 4, 5, …, 2X, 2X+ 1, …, 2K-2, 2K- 1, (2k has been erased), 2K+ 1, 2K+2, …, 2y-