Question

[Weekend Challenge] Mary studies at least 1 hour per day, but no more than 11 hours per week.

Prove that in the next seven weeks, there exists some period of consecutive days where Mary studies exactly 20 hours.

Answer 1

Could this be proved using pigeonhole principle?

Answer 2

Yes! looks it needs a little extra work too...

Answer 3

I may just use program to prove lol

Answer 4

Ahh I'm sure programming solution would be interesting too :)

Answer 5

If mary is studying at least 1 hour every day, then for 7 days her minimum study time in 7hours but max is 11 hours so the remaining 4 hours, even if they are split evenly, there's then at least one day where she's studying for 2 hours...and the max she can study in one day is 5hours and no. of hours for 2 weeks is 22hours...ahh im so lost :)

Answer 6

where do you even find such questions?do you make them up?

Answer 7

Looks like a good start ! that also shows that the number of hours studied is between 1 and 77 !

this question is a nice application of pigeonhole principle
http://en.wikipedia.org/wiki/Pigeonhole_principle

Answer 8

Is mary studying 11 hours every week or is that just a limit

Answer 9

11 hours every week is just a limit

Answer 10

Are you really a professor? @ganeshie8

Answer 11

In next 7 weeks max hours she can study = 77 hours
min hours = 49 hours
remaining hours 28 hours
only one day possible in which she can study 20 hours and next day 10 hours
unless we rule out the condition of contuinues to study after 12PM :P

Answer 12

Answer? I couldn't think of one.

Answer 13

At least give some hints....

Answer 14

I'll post a solution shortly...

Answer 15

@ganeshie8 Solution?

Answer 16

@ganeshie8 solution? :3

Answer 17

Hey sorry for the delay. see
http://openstudy.com/study#/updates/5042dff7e4b060a4c5a30bff