analog spruce
a grandmaster plays at least one game of chess a day to keep fit, but no more than 10 a week to avoid fatigue. prove that if he plays long enough, there will be a continuous period of days during which he has played exactly 21 times. Translation for what you see : a index i is the amount of game played until the day i. We deduce… for k sufficiently big, the inequality 2k >= 21 + 10 x k/7 becomes true. Thus there exists two indexes i and j such that aj = ai + 21. The master will have played 21 games during the period spanning between the day i + 1 and the day j included.
maiden hemlock