0

We are given a set of $101$ positive integers that sum to $300$.

Since summation of $101$ distinct numbers cannot be $300$, repetition among the $101$ positive integers exists.

Can we choose a group of numbers from the $101$ positive integers such that the sum of the elements in the group is $100$?

If not, please tell me a counter-example.

Winther
  • 25,313
user331899
  • 482
  • Choose the numbers $1001, 1002,\ldots, 1101$. – vadim123 May 26 '16 at 04:03
  • I edited the question. Please check that I did not change the intended meaning. – Winther May 26 '16 at 04:19
  • 3
    Let ${x_1,x_2,\ldots,x_{101}}$ be the elements and consider the $101$ subsets ${x_1},{x_1,x_2}$, $\ldots$, ${x_1,x_2,\ldots,x_{101}}$. Now consider the sum of the elements of these subsets $\mod 100$. For more info see this answer. – Winther May 26 '16 at 04:47

0 Answers0