Baltic Way 1993 · Problem 11
Combinatorics
An equilateral triangle is divided into congruent equilateral triangles. A spider stands at one of the vertices, a fly at another. Alternately each of them moves to a neighbouring vertex. Prove that the spider can always catch the fly.
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Review
Topics
Games and strategies · Algorithms and processes · Pigeonhole and extremal arguments
Solutions
Solution
Solution:
Assume that the big triangle lies on one of its sides. Then a suitable strategy for the spider will be as follows:
(1) First, move to the lower left vertex of the big triangle.
(2) Then, as long as the fly is higher than the spider, move upwards along the left side of the big triangle.
(3) After reaching the horizontal line where the fly is, retain this situation while moving to the right (more precisely: move "right", "right and up" or "right and down" depending on the last move of the fly).
Contest context
Results from Baltic Way 1993
8 teams
- Mean score
- 3.5 / 5
- Scores of 4 or 5
- 5 / 8
- Estonia
- 5 / 5
Score distribution
All team scores
| Team | Score |
|---|---|
| Poland | 2 / 5 |
| Latvia | 5 / 5 |
| Estonia | 5 / 5 |
| Sweden | 4 / 5 |
| Lithuania | 1 / 5 |
| Finland | 4 / 5 |
| Iceland | 2 / 5 |
| Denmark | 5 / 5 |