Question

Linda has 5 weeks to prepare for her final. Her friend has volunteered to help her for either 15min or 30min every day until the test but not for more than 15 hours total. Show that during some period of consecutive days, Linda and her friend will study for exactly 8.75 hours.

Please do not prove by evaluating anything since this is asking to prove for every different combinations of 15min or 30min studying there should be some consecutive days they will study for 8.75 hours. Please keep in mind that they should study everyday (meaning all 5x7 = 35 days, there is no days that they don't study) and that they can do combinations of 15 or 30 min study days. We are asked to prove this using Pigeon Hole Principle and with the use of sets/subtracting and adding sets.

Answer 1

Solution: 8hrs 4-5 ming Frst S 8.75 haurs 525 mins Totat Study =15 Dys of Somins mins IS OY 35 days Zinda have 5x for (lodays-30mins) wi t Study Linda her fricnd 15 mins and for s days hrs 525 15xIS OX30