MathDB

(a)

There are two sequences of numbers, with

2003

consecutive integers each, and a table of

2

rows and

2003

columns

\begin{array}{|c|c|c|c|c|c|} \hline\ \ &\ &\ &\cdots\cdots&\ &\ \\ \hline \ &\ &\ &\cdots\cdots&\ &\ \\ \hline \end{array}

Is it always possible to arrange the numbers in the first sequence in the first row and the second sequence in the second row, such that the sequence obtained of the

2003

column-wise sums form a new sequence of

2003

consecutive integers?

(b)

What if

2003

is replaced with

2004

Problem Statement