MathDB

5

Part of 2009 Argentina National Olympiad

Problems(1)

2009 integers around a circle

Source: 2009 Argentina OMA Finals L3 p5

1/15/2023
Around a circle are written2009 2009 integers, not necessarily distinct, so that if two numbers are neighbors their difference is 11 or 22 . We will say that a number is huge if it is greater than its two neighbors, and that it is tiny if it is less than its two neighbors. The sum of all the huge numbers is equal to the sum of all the tiny numbers plus 18101810. . Determine how many odd numbers there can be around the circumference.
combinatorics