Question: A chess master has 35 days to prepare for a tournament. She will play no more than 50 games. She also wishes to play at

A chess master has 35 days to prepare for a tournament. She will play no more than 50 games. She also wishes to play at least 1 games per day. Show that no matter how she schedules her preparation, there is a succession of days during which she will have played exactly 19 games.

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