MathDB

The natural numbers

0, 1, 2, 3, . . .

are written on the square table 2015\times 2015 in a circular order (anti-clockwise) such that

0

is in the center of the table. The rows and columns are labelled from bottom to top and from left to right respectively. (see figure below) 1. The number

2015

is in which row and which column? 2. We are allowed to perform the following operations: First, we replace the number

0

in the center by

14

, after that, each time, we can add

1

to each of

12

numbers on

12

consecutive unit squares in a row, or

12

consecutive unit squares in a column, or

12

unit squares in a rectangle

3\times 4

. After a finite number of steps, can we make all numbers on the table are multiples of

2016

? https://cdn.artofproblemsolving.com/attachments/c/d/223b32c0e3f58f62d0d40fa78c09a2cd035ed5.png

Problem Statement