Basically, your strategy for a given question might as well depend only on which of the candidates agreed with each other on the answer. (In that for any two questions with the same agreements, agreeing with candidate 1 has the same expected score, and since expectation is linear, you might as well do the same for each).
For the two person situation, you therefore have 4 different strategies based on : * if the two students put the same answer, put the same answer as them or the opposite answer : * if the two students put different answers, put the same as student 1 or student 2. These four strategies work out as: (same => same, different => student 1): copy student 1 (same => same, different => student 2): copy student 2 (same => opposite, different => student 1): write the exact opposite of student 2 (same => opposite, different => student 2): write the exact opposite of student 1 For the three person situation, there are 16 different strategies which are: 1-3: copy student 1, 2 or 3 4-6: write the exact opposite of student 1,2 or 3 7: go with the majority 8: disagree with the majority 9: if they all agree, write the same as them, otherwise write the opposite of student 1 10: if they all agree, write the same as them, otherwise write the opposite of student 2 11: if they all agree, write the same as them, otherwise write the opposite of student 3 12-14: write the opposite of strategy 9-11 15: if they all agree, write the same as them, otherwise write the opposite of the majority 16: if they all agree, write the opposite of them, otherwise write the same as the majority On Sun, Apr 25, 2021 at 4:27 PM Jakub Nogły <choci...@gmail.com> wrote: > Hi all, > > At the beginning I wanted to thank the code jam team for great problems. > Keep up the good work! > > I have a question regarding the "Hacked Exam". The solution I submitted > for the competition was to select the best or the worst score from the > samples and return the same or "opposite" string (replace T with F and F > with T). The expected score was the exact score this exam answer would have > achieved. To my surprise it passed both tests for N=2. Obviously it did not > work for the largest test case. > > Since this "solution" was not mentioned in the analysis I am curious if it > was accident that it passed or indeed for N=2 we can't do better than > replicating the best/worst answer. I could not prove the latter, maybe > someone on this list has more idea about that? > > My hypothesis is that if question can have B possible answers then if we > get B or less samples we can't do better than replicating worst/best one. > In other words we can't get more insights about any of the questions in a > sense. > > Thank you, > Jakub > > -- > -- You received this message because you are subscribed to the Google > Groups Code Jam group. To post to this group, send email to > google-code@googlegroups.com. To unsubscribe from this group, send email > to google-code+unsubscr...@googlegroups.com. For more options, visit this > group at https://groups.google.com/d/forum/google-code?hl=en > --- > You received this message because you are subscribed to the Google Groups > "Google Code Jam" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to google-code+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/google-code/CABoOB-XWUih3Fm48cd5N1xCy35VndbmLOnMim2isyR0ASvSWow%40mail.gmail.com > <https://groups.google.com/d/msgid/google-code/CABoOB-XWUih3Fm48cd5N1xCy35VndbmLOnMim2isyR0ASvSWow%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- -- You received this message because you are subscribed to the Google Groups Code Jam group. To post to this group, send email to google-code@googlegroups.com. To unsubscribe from this group, send email to google-code+unsubscr...@googlegroups.com. For more options, visit this group at https://groups.google.com/d/forum/google-code?hl=en --- You received this message because you are subscribed to the Google Groups "Google Code Jam" group. To unsubscribe from this group and stop receiving emails from it, send an email to google-code+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/google-code/CAECKw-N%3DYKXZ7gFiRai0W93ZkD-tLE8zHHo4GXfek4wykCcTmw%40mail.gmail.com.
