Question

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.

Answer 1

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.