MathDB

Let

n

be a positive integer. Jadzia has to write all integers from

1

2n-1

on a board, and she writes each integer in blue or red color. We say that pair of numbers

i,j\in \{1,2,3,...,2n-1\}

, where

i\leqslant j

, is

<span class='latex-italic'>good</span>

if and only if number of blue numbers among

i,i+1,...,j

is odd. Determine, in terms of

n

, maximal number of good pairs.

Problem Statement