MathDB

A game is played between two players on a

10 \times 10

checkerboard. They move alternately, the first player marking

X

s on vacant cells and the second

O

s. When all

100

cells have been marked, they calculate two numbers

C

and

Z

C

is the total number of five consecutive

X

s in a row, a column or a diagonal, so that

6

consecutive

X

s contribute a count of

2

C

7

consecutive

X

s contribute

3

, and so on. Similarly,

Z

is the total number of five consecutive Os. The first player wins if

C > Z

, loses if

C < Z

and draws if

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)

Problem Statement