Ivan Shishkin, Rye (1878)

Problems/CombinatoricsReviewed

Forest tournament

by Sequoia·
26
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
·
English
EnglishFrançais

A tournament has a pool with 4 teams : Squirrels, Wolves, Foxes, Ants.
Each team plays against all other teams.
A victory counts for 3 points, a draw counts for 1 point, and no point for defeat.

  1. How many matches are there ?

  2. How many configurations are there for the ranking ?
    Example of a configuration : Foxes (9) Ants (4) Wolves (4) Squirrels (0)

  3. How many configurations are there regardless of the team ?
    Example : A team gets 9 points, two teams get 4, one team gets no points.

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