MathDB

Zeros and ones are placed in each square of a rectangular board. Such a board is said to be varied if each row contains at least one

0

and at least two

1

s. Given n

\geq 3,

find all integers

k>1

with the following property:
The columns of each varied board of

k

rows and n columns can be permuted so that in each row of the new board the

1

s do not form a block (that is, there are at least two

1

s that are separated by one or more

0

s).

3