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The materials for the include problems and solutions for both the Fall and Spring rounds.
For additional preparation, you can browse the full archive of past tasks or review categorized problems on Shkolkovo . Fourty seventh Tournament of Towns, 2025 – 2026
The competition is split into two main seasons, each offering a "Basic" (easier) and a "Senior/Advanced" (harder) paper. Basic Variant: October 5, 2025. Advanced Variant: October 19, 2025. Spring Round (2026): Basic Variant: March 1, 2026. Advanced Variant: March 15, 2026. Final Oral Round: March 29, 2026. Sample Problems from the 47th Tournament The materials for the include problems and solutions
You can find the official papers, including specific versions for different grade levels and difficulty settings, on the Official Tournament of Towns website and the University of Toronto's mirror site .
A problem involving a 60-digit number made of ones and eights, requiring a proof of divisibility by a 30-digit number consisting only of nines. Basic Variant: October 5, 2025
A geometry problem about a regular octahedron with its faces divided into smaller triangles, asking for the maximum number of non-adjacent triangles that can be colored.
table filled with plus and minus signs, where they take turns crossing out rows and columns. Advanced Variant: March 15, 2026
A game theory problem between Alice and Bob involving a