MathDB

A triangular table with

n

rows and

n

columns is given, the

i

-th row ends with a field in the

v

-th column. In each field of the table, some of the numbers

1,2,..., n

are written such that for each

k \in {1, 2,..., n}

all the numbers

1,2,..., n

occur in the union of the

k

-th row and the

k

-th column. Prove that for odd

n

, each of the numbers

1,2,..., n

is written in the last box of a row. https://cdn.artofproblemsolving.com/attachments/f/9/2aed55628edb1505c7de27c152127b04d8d991.png

Problem Statement