MathDB

Let

n

be a positive integer. Find the greatest possible integer

m

, in terms of

n

, with the following property: a table with

m

rows and

n

columns can be filled with real numbers in such a manner that for any two different rows

\left[ {{a_1},{a_2},\ldots,{a_n}}\right]

and

\left[ {{b_1},{b_2},\ldots,{b_n}} \right]

the following holds:

\max\left( {\left| {{a_1} - {b_1}} \right|,\left| {{a_2} - {b_2}} \right|,...,\left| {{a_n} - {b_n}} \right|} \right) = 1

Poland (Tomasz Kobos)

2