Y by Wizard_32, Adventure10, megarnie, Mango247, kiyoras_2001, and 3 other users
A rectangular array of numbers is given. In each row and each column, the sum of all numbers is an integer. Prove that each nonintegral number
in the array can be changed into either
or
so that the row-sums and column-sums remain unchanged. (Note that
is the least integer greater than or equal to
, while
is the greatest integer less than or equal to
.)







This post has been edited 1 time. Last edited by orl, Oct 23, 2004, 12:58 PM