Enigmatic Code

Programming Enigma Puzzles

Puzzle #168: Bone idle

From New Scientist #3387, 21st May 2022 [link] [link]

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?


One response to “Puzzle #168: Bone idle

  1. Jim Randell 21 May 2022 at 8:41 am

    The paper has 11 questions chosen from 18 potential topics.

    So there are 7 topics that do not appear on the paper.

    We assume that it is possible to get top marks by answering only 4 of the questions.

    The worst case scenario is that Rick revises the 7 topics that aren’t on the paper, plus 4 others (which must be on the paper), so 11 topics in all.

    Solution: Rick should revise 11 of the topics.

    In the general case, if there are q questions chosen from t topics, and you must answer k questions.

    Then the worst case is that Rick revises the (t − q) topics that aren’t on the paper, plus k others (that are), so (t − q + k) topics in total.

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