Baltic Way 1996 · Problem 16
Combinatorics
On an infinite checkerboard, two players alternately mark one unmarked cell. One of them uses , the other . The first who fills a square with his symbols wins. Can the player who starts always win?
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Review
Topics
Colorings and configurations · Pigeonhole and extremal arguments · Games and strategies
Solutions
Solution
Solution:
Divide the plane into dominoes in the way indicated by the thick lines in Figure 2. The second player can respond by marking the other cell of the same domino where the first player placed his mark. Since every square contains one whole domino, the first player cannot win.
Figure 2
Contest context
Results from Baltic Way 1996
10 teams
- Mean score
- 1.7 / 5
- Scores of 4 or 5
- 3 / 10
- Estonia
- 0 / 5
Score distribution
06
10
21
30
40
53
All team scores
| Team | Score |
|---|---|
| Poland | 0 / 5 |
| Latvia | 5 / 5 |
| Sweden | 5 / 5 |
| Denmark | 5 / 5 |
| St. Petersburg | 0 / 5 |
| Finland | 0 / 5 |
| Norway | 2 / 5 |
| Lithuania | 0 / 5 |
| Estonia | 0 / 5 |
| Iceland | 0 / 5 |