Question 24
Davide normally needs at least 8 hours of sleep each night. If one night he sleeps $k$ hours less than he needs, he needs $k$ extra hours of sleep on each of the next $k$ nights. Each night he sleeps an integer number of hours not exceeding his need. For example, if he needs 8 hours on Monday but sleeps 7, he needs 9 on Tuesday. If he needs 8 on Wednesday but sleeps 6, he needs at least 10 on Thursday and Friday; if he sleeps only 9 on Thursday, he needs 11 on Friday: 8, plus 2 for Wednesday's deficit, plus 1 for Thursday's.
On a certain Monday night Davide needs 8 hours, and the same holds on the following Monday. During the intervening week there were 7 hours when he needed sleep but did not sleep. What is the minimum total number of hours he slept on the seven nights Monday through Sunday?
On a certain Monday night Davide needs 8 hours, and the same holds on the following Monday. During the intervening week there were 7 hours when he needed sleep but did not sleep. What is the minimum total number of hours he slept on the seven nights Monday through Sunday?