MathDB

There is

207

boxes on the table which numbered

1,2, \dots , 207

respectively. Firstly Aslı puts a red ball in each of the

100

boxes that she chooses and puts a white ball in each of the remaining ones. After that Zehra, writes a pair

(i,j)

on the blackboard such that

1\leq i \leq j \leq 207

. Finally, Aslı tells Zehra that for every pair; whether the color of the balls which is inside the box which numbered by these numbers are the same or not. Find the least possible value of

N

such that Zehra can guarantee finding all colors that has been painted to balls in each of the boxes with writing

N

pairs on the blackboard.

Problem Statement