Combinatorics · Combinatorial games · Pairing strategy · Modular arithmetic · Powers of three · Parity of the move count
In the expression
\[ *\,1 * 3 * 3^{2} * 3^{3} * \cdots * 3^{1997} * 3^{1998} \]
Arkadije and Branislav take turns replacing one of the stars by \(+\) or by \(-\), one star per move, until no star is left. Branislav is trying to make the resulting number divisible by \(7\). Arkadije moves first. Can he stop him?
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Serbian Republic Competition (Republicko takmicenje) 1998, high school grade I, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source