Baltic Way 2022 · Problem 9
Combinatorics
Five elders are sitting around a large bonfire. They know that Oluf will put a hat of one of four colours (red, green, blue or yellow) on each elder's head, and after a short time for silent reflection each elder will have to write down one of the four colours on a piece of paper. Each elder will only be able to see the colour of their two neighbours' hats, not that of their own nor that of the remaining two elders' hats, and they also cannot communicate after Oluf starts putting the hats on.
Show that the elders can devise a strategy ahead of time so that at most two elders will end up writing down the colour of their own hat.
When you’re ready
Review material becomes available with the next Daily.
Review
Topics
Games and strategies · Colorings and configurations · Pigeonhole and extremal arguments
Solutions
No verified local solution is currently available.
Contest context
Results from Baltic Way 2022
10 teams
- Mean score
- 0.7 / 5
- Scores of 4 or 5
- 1 / 10
- Estonia
- 0 / 5
Score distribution
All team scores
| Team | Score |
|---|---|
| Poland | 0 / 5 |
| Germany | 0 / 5 |
| Lithuania | 0 / 5 |
| Estonia | 0 / 5 |
| Denmark | 5 / 5 |
| Latvia | 0 / 5 |
| Sweden | 1 / 5 |
| Norway | 0 / 5 |
| Finland | 1 / 5 |
| Iceland | 0 / 5 |