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# Wrong Problem in the Contest 'Coding Hours'

 1 In the contest COHR2018, the problem 'Chef And His Algorithm' is probably wrong. The problem asks us to compute the minimum length of a string which consists of all the permutations of the given string, if the latter has all unique characters. This problem is the same as the Minimal Superpermutation Problem, and it stands unsolved for $n > 5$ as of now. The answer to the problem was conjectured to be the following value by D. Ashlock and J. Tillotson: $$\sum_{i = 1}^n i!$$ The conjecture has been verified for $n \leqslant 5$, but it was later proven wrong for $n \geqslant 6$. The value of the above sum for $n = 6$ is $873$, but Robin Houston provided a counterexample, which was a superpermutation of length $872$, one less than the conjectured length, to disprove the conjecture. This paper explains the problem and the conjecture, and proof that the conjecture is wrong, in detail. Quoting from the paper: The minimal length is still unknown for $n ≥ 6$, but we can show that for all $n ≥ 6$ it is strictly less than the conjectured length $\sum_{i = 1}^n i!$ In the contest, what people have done for this problem is, they have printed the conjectured length for $n \leqslant 5$, and one less than the conjectured length for $n > 5$. However, "strictly less than" the conjectured length does not mean one less than the conjectured length. So I request @admin to do something about it. Probably remove the problem and its submissions from CodeChef, if possible. asked 06 Aug, 19:56 56●4 accept rate: 8% 2 Exactly what I wanted to say finally someone else did xD (06 Aug, 20:04) 1 Hi, thanks for reporting this. We are looking into it. (10 Aug, 18:25) admin ♦♦0★ @admin @vijju123 Is there any progress on this issue? (15 hours ago) Asking @admin. (14 hours ago)
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question asked: 06 Aug, 19:56

question was seen: 198 times

last updated: 15 hours ago