MathDB

Write down

1, 2, 3, ... , 2015

in a row on a whiteboard. Every minute, select a pair of adjacent numbers at random, erase them, and insert their sum where you selected the numbers. (For instance, selecting

3

and

4

from

1, 2, 3, 4, 5

would result in

1, 2, 7, 5

.) Repeat this process until you have two numbers remaining. What is the probability that the smaller number is less than or equal to

2015

Problem Statement