It's false, right?Yes, I have many ideas, but, as my wife will explain with examples, most are very bad.
Still, I might start by redefining the problem. Call a ”week” five consecutive days. Now the problem is that over six consecutive weeks, he played exactly 45 games in total, and he played at least 5 games each week. Now show that there must have been at least one week when he played exactly 14 games.
EDIT: What was the complete and exact wording of the problem?
For weeks one through five, he played five games each week. Therefore he played twenty in week six.
20=14.
My first concern about the problem is, are "practice", "study", and "train" meant to be synonyms? I suppose so, but this isn't written carefully.Hello. Magnus Carlsen practiced chess at least once a day for 30 consecutive days, and in
those 30 days he studied exactly 45 times in total. Prove that there are 5 consecutive days in which
Magnus trained exactly 14 times.
Any ideas?
The 5 consecutive days don't have to be one of the "weeks" you break it into; they could span parts of two weeks.Still, I might start by redefining the problem. Call a ”week” five consecutive days. Now the problem is that over six consecutive weeks, he played exactly 45 games in total, and he played at least 5 games each week. Now show that there must have been at least one week when he played exactly 14 games.
For weeks one through five, he played five games each week. Therefore he played twenty in week six.
20=14.
I believe it is: if he practiced 2 times/day on odd days and 1 time/day on even days then any stretch of 5 consecutive days will have 7 or 8 practices.It's false, right?
YesMy first concern about the problem is, are "practice", "study", and "train" meant to be synonyms? I suppose so, but this isn't written carefully.
Yes, it’s obviously false under my simplification, but Dr. Peterson has pointed out that my simplification is not a useful one because the five consecutive days need not fall in any of what I proposed as a “week.” The five consecutive days could be split across TWO weeks.It's false, right?