Number picking is the problem of counting the distinct sums obtained by choosing 
balls without replacement from 
balls labeled 1 through 
, where 
is a positive integer.
The sums run through every integer from 
to 
, so their number is 
. For 
, 2, 3, ..., the counts are 2, 5, 10, 17, 26, ... (OEIS A002522).
Number Picking
See also
Number Guessing, Real Number PickingExplore with Wolfram|Alpha
References
Sloane, N. J. A. Sequence A002522 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Number PickingCite this as:
Weisstein, Eric W. "Number Picking." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NumberPicking.html