Let S be a set consisting of 31 positive real numbers. For each non-empty subset A ⊂ S let
f(A) be the product of all elements of A. We say that a subset A ⊂ S is rational if f(A) is
a rational number. We say that a subset A ⊂ S is irrational if f(A) is an irrational number.
Is there any set S having exactly 2023 rational subsets? Is there any set S having exactly
2025 irrational subsets?
Correct Solutions by,
- Toshihiro Shimizu Kawasaki, Japan
- Magnus Jakobsson Lund, Sweden
- Jepbar Asgarov Aşgabat, Turkmenistan
- Alper Balcı Ohio State University
- Hamza Akdeniz Bilkent University
- Mehmet Samet Ödük METU
- Arda Karahan Trabzon Fen Lisesi
Solution: 2412a.pdf (bilkent.edu.tr)