generated from Timothee/TFJM-Template
Notations pb 7
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\q a) (facile/moyen) Toutes les configurations s'équivalent. Le résultat est $N(N-1)+(N-1)(N-2)+(N-2)(N-3)+...+2 \times 1 = (N-1)N(N+1)/3$.
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\q a) (facile/moyen) Toutes les configurations s'équivalent. Le résultat est $n(n-1)+(n-1)(n-2)+(n-2)(n-3)+...+2 \times 1 = (n-1)n(n+1)/3$.
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b) (facile) Max : $2N+(2N-1)+...+(N+1)=N(3N+1)/2$.
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b) (facile) Max : $2m+(2m-1)+...+(m+1)=m(3m+1)/2$.
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Min : $2N+(2N-2)+(2N-4)+...+2=N(N+1)$.
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Min : $2m+(2m-2)+(2m-4)+...+2=m(m+1)$.
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c) (moyen) Max, $N=2n$ pair : $2(2n+(2n-1)+...+(n+1))=n(3n+1)$.
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c) (moyen) Max, $n=2k$ pair : $2(2k+(2k-1)+...+(k+1))=k(3k+1)$.
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Max, $N=2n+1$ impair : $2(2n+1+2n+...+n+2)+n+1=(n+1)(3n+1)$.
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Max, $n=2k+1$ impair : $2((2k+1)+2k+...+(k+2))+k+1=(k+1)(3k+1)$.
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Min : $2N+(N-1)+(N-2)+...+2=(N^2+3N-2)/2$.
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Min : $2n+(n-1)+(n-2)+...+2=(n^2+3n-2)/2$.
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