Question: Linda has 5 weeks to prepare for herCSCA67 final. Her friend has volunteered to help her for either15min or 30min every day until the test but not for more than 15hours total. Show that during some period of consecutive days,Linda and her help will study for exactly 8 3/4 hours.
Answer: We can solve this by letting airepresent the number of quarter hours Linda studies on day i. Thenthere are 5x7 = 35 days that Linda studies. Now we define 35 sums:s1 = a1, s2 = a1 +a2, s3 = a1 +a2 +a3. Then if one of these sumsequals 8 ∗ 4+3 = 35 quarter hours, we are done. If not, then thereare 35 sums (pigeons) and we set our holes to be the possibleremainders for each sum when divided by 35, we have the values from1..34 or 34 holes. Therefore there are two pigeons in one hole, ie,two sums that when divided by 35 have the same remainder. If wesubtract the smaller sum from the larger we get a continuous subsetof days (by the way we designed the si and this difference must bedivisible by 35. Since no sum is larger than 60 and the differenceis a multiple of 35, this multiple cannot be larger than 1.Therefore we have a set of consecutive days totally 8 3 4hours.
My question: Can someone help me to under standand solve this question in proper way by using php. I dontunderstand how answer says, \"35 sums (pigeons) and we set our holesto be the possible remainders for each sum when divided by 35, wehave the values from 1..34 or 34 holes\"
