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Tournament Of Towns
1996 Tournament Of Towns
(487) 5
(487) 5
Part of
1996 Tournament Of Towns
Problems
(1)
TOT 487 1996 Spring J O5 2player game on 10x10 chessboard
Source:
7/9/2024
A game is played between two players on a
10
×
10
10 \times 10
10
×
10
checkerboard. They move alternately, the first player marking
X
X
X
s on vacant cells and the second
O
O
O
s. When all
100
100
100
cells have been marked, they calculate two numbers
C
C
C
and
Z
Z
Z
.
C
C
C
is the total number of five consecutive
X
X
X
s in a row, a column or a diagonal, so that
6
6
6
consecutive
X
X
X
s contribute a count of
2
2
2
to
C
C
C
,
7
7
7
consecutive
X
X
X
s contribute
3
3
3
, and so on. Similarly,
Z
Z
Z
is the total number of five consecutive Os. The first player wins if
C
>
Z
C > Z
C
>
Z
, loses if
C
<
Z
C < Z
C
<
Z
and draws if
C
=
Z
C = Z
C
=
Z
. Does the first player have a strategy which guarantees (a) a draw or a win (b) a win regardless of the counter-strategy of the second player?(A Belov)
combinatorics