Number theory · Prime factorisation · Exponent counting · Extremal problems · Dice products
Oliver rolled an ordinary die \(100\) times and multiplied together all \(100\) numbers that came up on top. The product he obtained was \(6^{70}\). What is the smallest possible number of rolls on which the die showed \(6\)?
- A \(10\)
- B \(12\)
- C \(24\)
- D \(30\)
- E \(35\)
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2024, 1. letnik, category A, problem A1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source