Jessica is studying combinatorics during a 7-week period. She will study a positive integer number of hours every day during the 7 weeks (so, for example, she won't study for 0 or 1.5 hours), but she won't study more than 11 hours in any 7-day period. Prove that there must exist some period of consecutive days during which Jessica studies exactly 20 hours.

Question

Kai Harvey

Mathematics

1 May, 05:59

Jessica is studying combinatorics during a 7-week period. She will study a positive integer number of hours every day during the 7 weeks (so, for example, she won't study for 0 or 1.5 hours), but she won't study more than 11 hours in any 7-day period. Prove that there must exist some period of consecutive days during which Jessica studies exactly 20 hours.

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Answers (1)

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Yukon · Answer 1

Step-by-step explanation:

Given that Jessica is studying combinatorics during a 7-week period. She will study a positive integer number of hours every day during the 7 weeks

Also given that she will not study more than 11 days in any 7 week period.

Then she can select from 1,2 ... 11 for the 49 days

Thus she has to select 9 and 11 from the available for any two consecutive days

this will give a total of 20 hours.

There must exist atleast some period of consecutive days during which Jessica studies exactly 20 hours.