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Tournament Of Towns
1988 Tournament Of Towns
(173) 6
(173) 6
Part of
1988 Tournament Of Towns
Problems
(1)
TOT 173 1988 Spring J6 infinite squares on plane, numbers inside
Source:
5/9/2020
The first quadrant of the Cartesian
0
−
x
−
y
0-x-y
0
−
x
−
y
plane can be considered to be divided into an infinite set of squares of unit side length, arranged in rows and columns , formed by the axes and lines
x
=
i
x = i
x
=
i
and
y
=
j
y = j
y
=
j
, where
i
i
i
and
j
j
j
are non-negative integers. Is it possible to write a natural number
(
1
,
2
,
3
,
.
.
.
)
(1,2, 3,...)
(
1
,
2
,
3
,
...
)
in each square , so that each row and column contains each natural number exactly once?(V . S . Shevelev)
combinatorics