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Show all threads Hide all threads Show all messages Hide all messages | mathematical proof of the solution SPOILERS!!! | lallala | 1870. Zinium 2 | 17 Feb 2016 18:13 | 1 | SPOILERS!!!SPOILERS!!! Do not look without solving the problem! let (xi,yi) are coordinates of n points. Following sets {xi} {yi} {xi+yi} {xi-yi} are some permutations of {1,2,...,n} by module n. if n%2==0 Then Sum(xi)+Sum(yi)=Sum(xi+yi) (mod n) it is not true since, n*(n+1)!=(n*(n+1))/2 (mod n) (since n -even) if n%3==0 Then Sum(xi*xi)+Sum(yi*yi)=Sum( (xi+yi)*(xi+yi) )+Sum( (xi-yi)*(xi-yi) ) it is not true since, ( n*(n+1)*(2n+1) )/3!=( 2*n*(n+1)*(2n+1) )/3 (mod n) (since n%3==0) Here, I used the fact that if (xi) is permutation of {1,2,...,n} by module n then sum of them is n*(n+1)/2 (mod n). Same with summing (xi*xi). | WA 6 ????? | Михаил | 1870. Zinium 2 | 15 Jan 2012 04:25 | 4 | Some tests: n - answer 15 - No 99 - No 23 - Yes 97 - Yes 16 - No wa20 BaJIuK 15 Jan 2012 04:25 if you have WA20 try this tests :) 25 YES 145 YES 9991 YES 9995 YES | Even numbers | Vitaliy Karelin | 1870. Zinium 2 | 20 Oct 2011 19:45 | 2 | Is it right, that on even numbers answer will always "No"? |
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