MathDB

An assignment of either a

0

or a

1

to each unit square of an

m

n

chessboard is called

fair

if the total numbers of

0

s and

1

s are equal. A real number

a

is called

beautiful

if there are positive integers

m,n

and a fair assignment for the

m

n

chessboard such that for each of the

m

rows and

n

columns , the percentage of

1

s on that row or column is not less than

a

or greater than 100\minus{}a. Find the largest beautiful number.

Problem Statement