Question

Al has 75 days to master discrete mathematics. He decides to study at least one
hour every day, but no more than a total of 125 hours. Show there must be a
sequence of consecutive days during which he studies exactly 24 hours.

Answer 1

generalized pigeonhole principle i bet

Answer 2

i think there may be some mistake here

Answer 3

125 hours divided by 75 days gives an average of \(\frac{5}{3}\) hour per day, so i cannot see why there is a sequence (or even one) day in which he must study 24 hours

Answer 4

Based on the information in the question, it is ridiculous to assume that he would even begin to approach 24 hours, let alone two days consecutively.

Answer 5

STudying 5/3 hours daily fulfills all requirements, and 24 hour requirements are not met...

Answer 6

Are you sure the problem doesn't ask for 25 hours consecutively? That would at least make more sense that 24 hours.

Answer 7

75 days, 125 hours total, at least one hour daily, and consecutive days where he studies 24 hours

Answer 8

It would seem that the question is erroneous in its assumption

Answer 9

It would certainly seem so. As written, the statement in question is false.