Gọi 7 số đã cho là: a, b, c, d, e, f, g. Giả sử \(a>b>c>d>e>f>g\)
Nếu \(c\ge16\) \(\Rightarrow\left\{{}\begin{matrix}b\ge17\\a\ge18\end{matrix}\right.\) \(\Rightarrow a+b+c\ge16+17+18=51\)
Nếu \(c\le15\) \(\Rightarrow\left\{{}\begin{matrix}d\le14\\e\le13\\f\le12\\g\le11\end{matrix}\right.\) \(\Rightarrow d+e+f+g\le14+13+12+11=50\)
\(\Rightarrow a+b+c\ge100-50=50\)
Vậy có ĐPCM