2003 OIM Problems/Problem 1

Problem

a) There are two sequences, each of 2003 consecutive integers, and a board with 2 rows and 2003 columns

Decide if it is always possible to distribute the numbers of the first sequence in the first row and those of the second sequence in the second row, in such a way that the results obtained by adding the two numbers in each column form a new sequence of 2003 consecutive numbers.

b) What if 2003 is replaced by 2004?

In both a) and b), if the answer is affirmative, explain how you would distribute the numbers, and if the answer is negative, justify why.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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