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#168 Bone idle

University student Rick Sloth has spent his life avoiding work, and even though it is exam season he has no intention of mending his lazy ways.

He is studying palaeontology, which he thought might be an easy option when he signed up for it, as he loves dinosaurs, but he has now discovered that it requires rather more study than he was expecting.

It turns out there are 18 topics in the syllabus and his end-of-year exam will feature 11 essay questions, each on a different topic. Fortunately for Rick, candidates are only required to answer four questions in total.

Rick wants to keep his exam preparation to a bare minimum, while still giving himself a chance of getting full marks.

How many topics does he need to revise if he is to be certain that he will have at least four questions that he can tackle?

And can you come up with a general formula for the minimum number of topics you need to study based on the number of exam questions and topics in the syllabus?

Solution next week

#167 This escalated quickly

Solution

Jack should choose the stairs. No matter how much faster he is than the escalator (up or down), he will lose more time going against it than he will gain running with it.

Suppose it takes him T seconds to climb the stairs. If, for example, the escalator moves at half Jack鈥檚 running speed, then going up the up escalator improves his speed by 50 per cent, and he will make it to the top in 2/3 the time (2/3 T) to climb the stairs. Coming down, however, it will halve his speed, so he takes twice as long to go down as to descend the stairs (2T).

Up and down on the stairs would take about 2T total, up and down on the up escalator would be 2T + 2/3 T. A slight difference in his up and down running speed might make one escalator a better choice than the other, but the stairs are still the best choice overall.