Four Decision Trees

Four Decision Trees

English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].

Task 4 of the school stage of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence (region group I), grades 9–11. The official answer and solution are in a separate file.

Four simple rules are given in the form of “question trees”, which, depending on various features, assign an object the label 0 or 1. An object is described by three features:
$A$ — a binary feature: 0 or 1;
$B$ — shape: circle, square or triangle;
$C$ — a number (may be any real number)

Tree 1:

[Figure: see the original statement.]

• $B$ = circle?
  • no → $A = 0$?
    • no → Label 0
    • yes → Label 1
  • yes → $C \ge 3$?
    • no → Label 1
    • yes → Label 0

Tree 2:

[Figure: see the original statement.]

• $B$ = square?
  • no → $C \ge 4$?
    • no → Label 0
    • yes → Label 1
  • yes → $A = 0$?
    • no → Label 0
    • yes → Label 1

Tree 3:

[Figure: see the original statement.]

• $A = 1$?
  • no → $C = 3$?
    • no → Label 0
    • yes → Label 1
  • yes → $B$ = triangle?
    • no → Label 1
    • yes → Label 0

Tree 4:

[Figure: see the original statement.]

• $C \ge 2$?
  • no → $A = 1$?
    • no → Label 0
    • yes → Label 1
  • yes → $B$ = square?
    • no → Label 0
    • yes → Label 1

(The trees above are the translator's transcription of the four tree diagrams.)

Find the unique object (values of $A$, $B$, $C$) that receives label 1 from all four trees.

Scoring criterion: 4 points for each correct answer. Total — 12 points

Maximum score for the task — 12