A single-meeting round-robin chess tournament commenced with five players Adrian, Beau, Craig, Damian, and Elliott playing against each other exactly once.
At the end of the tournament Adrian came 1st, Beau came 2nd, Craig came 3rd, Damian came 4th, and Elliott came 5th.
Beau and Elliott shared their impressions as follows:
- Beau: "I am the only one who finished without a single loss."
- Elliott: "I am the only one who did not win a single game."
The rules were:
- A winner got a full point.
- For a draw each opponent got half a point, and:
- The ranking is decided only by looking at the points.
Reconstruct the tournament table from the clues mentioned above.
10 games are played, so the total points must equal 10.
Since A must lose at least one game, his maximum points are 3. Then B has a maximum of 2.5, C has a maximum of 2, D has a maximum of 1.5. That adds to 9, so D has a minimum of 1 point. Since C beats D, the scores must be
A 3, B 2.5, C 2, D 1.5 and E 1.
One Way:
A -- 3 points --wins vs CDE
B -- 2.5 points -- wins vs A and ties vs CDE
C -- 2 points -- wins vs E and ties vs BD
D -- 1.5 points -- ties vs BCE
E -- 1 point -- ties vs BD
I have not done the work to see if this solution is unique.
One way (solution)
