MathDB

Peter wrote

100

distinct integers on a board. Basil needs to fill the cells of a table

100\times{100}

with integers so that the sum in each rectangle

1\times{3}

(either vertical, or horizontal) is equal to one of the numbers written on the board. Find the greatest

n

such that, regardless of numbers written by Peter, Basil can fill the table so that it would contain each of numbers

(1,2,...,n)

at least once (and possibly some other integers).

Problem Statement