k=1,2,...,n.
a(1) + a(2) + ... + a(n) = 100.
= 10^100 -
- [a(1)*a(2) + a(1)*a(3) + ... + a(1)*a(n) + a(2)*a(3) + a(2)*a(4) + ... + a(2)*a(n) + ... + a(n-1)*a(n)]*10^99 +
+ [a(1)*a(2)*a(3) + a(1)*a(2)*a(4) + ... + a(1)*a(2)*a(n) + a(1)*a(3)*a(4) + a(1)*a(3)*a(5) + ... + a(1)*a(3)*a(n) + ... + a(1)*a(n-1)*a(n) + a(2)*a(3)*a(4) + a(2)*a(3)*a(5) + ... + a(2)*a(3)*a(n) + a(2)*a(4)*a(5) + ... + a(2)*a(n-1)*a(n) + ... + a(n-2)*a(n-1)*a(n)]10^98 +
+ ... +
+ (-1)^(n+1)[a(1)*a(2)*...*a(n)]10^(100-n+1)