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Omni-MATH / Two players play the following game. The first player starts by writing either…

Problem

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problem

Two players play the following game. The first player starts by writing either 00 or 11 and then, on his every move, chooses either 00 or 11 and writes it to the right of the existing digits until there are 19991999 digits. Each time the first player puts down a digit (except the first one) , the second player chooses two digits among those already written and swaps them. Can the second player guarantee that after his last move the line of digits will be symmetrical about the middle digit? (I Izmestiev)
Plain-text mathematical notation (without MathML)
Two players play the following game. The first player starts by writing either 0 or 1 and then, on his every move, chooses either 0 or 1 and writes it to the right of the existing digits until there are 1999 digits. Each time the first player puts down a digit (except the first one) , the second player chooses two digits among those already written and swaps them. Can the second player guarantee that after his last move the line of digits will be symmetrical about the middle digit? 

(I Izmestiev)
Original LaTeX notation
Two players play the following game. The first player starts by writing either $0$ or $1$ and then, on his every move, chooses either $0$ or $1$ and writes it to the right of the existing digits until there are $1999$ digits. Each time the first player puts down a digit (except the first one) , the second player chooses two digits among those already written and swaps them. Can the second player guarantee that after his last move the line of digits will be symmetrical about the middle digit? 

(I Izmestiev)

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Source and history

task_id
bd4bc574-f5e9-58fe-9d03-dd15ef3ed9bc
task_key
test--bd4bc574-f5e9-58fe-9d03-dd15ef3ed9bc
task_revision_id
1
config / split
/ test

Official source

initial import