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.
generalized pigeonhole principle i bet
i think there may be some mistake here
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
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.
STudying 5/3 hours daily fulfills all requirements, and 24 hour requirements are not met...
Are you sure the problem doesn't ask for 25 hours consecutively? That would at least make more sense that 24 hours.
75 days, 125 hours total, at least one hour daily, and consecutive days where he studies 24 hours
It would seem that the question is erroneous in its assumption
It would certainly seem so. As written, the statement in question is false.
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