The solution is from the net, in "my words",http://www.worldscibooks.com/etextbo...177_chap01.pdf

page: 16, #11

First, denote the largest chosen number from as , a can be .

Second, we add to our all chosen numbers, that would not change the result:

Say, if and are chosen ones, ; then by adding to and we will still get .

So by adding a to the largest chosen, , we will get .

Now, we have two cases, one is if one of other chosen numbers is from ,

if so, we are done, if , then .

The second case is if the other n+1 chosen numbers are from and .

Now, consider the following pairs:

(If is a asome above pair then is from and is from )

So, we have pairs, but we choose numbers, then there must to be one pair with two chosen elements.

Say, that is , , ,