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Any permutation of the rows and columns is treated as an "equivalent" board. Part 1: Matt chooses to go second. (Case A) If Ben takes 2 or 3 tokens, then Matt can turn it into a 2x2 board and win. (Case B) If Ben takes 1 token: $$\begin{array}{ccc} O & O & O \\ O & O & O \\ \_ & O & O \end{array}$$ then Matt can take 2 tokens to ...


Up to symmetries of the board, there aren't very many possible moves for the first player: Does this strategy work?


Let's name the lines. +---+---+ | K | +---+ L + J + | H I | + G +---+---+ | | +---+---+ F + | D E | + C + A +---+ | B | +---+---+ The winner can be found by analyzing the game regardless of the position. Now that we know the winner, who is which color? And Bob's last move would ...


Well maybe this kind of puzzle (Puzzles must not be from active competitions) belongs to this site, but I guess it is not "that kind" of competitive, so here is the answer: One can check it here


The player who can win is by this strategy:


First player wins Example:


Second player wins. After that, Then, On first player's second turn, In the end, Alternately,


I would suggest an alternate (simpler) strategy:


My solution... Images: Enclose 3 boxes: Enclose 2 boxes:


The player with the winning strategy is Strategy


My solution: Proof: 1) The optimal strategy is to... 2) If both are playing optimal... 3) Bonus:


There is no strategy that is guaranteed to ever win, thanks to the BOOM rule. If Alice picks $N = a^{124}\times b$, with $a$ and $b$ distinct primes, then $N$ has 250 factors. Bob's challenge is to determine $a$ and $b$. The problem is that if he determines the order of the factors before determing both $a$ and $b$, then the BOOM rule can prevent him from ...



I think that the solution is Strategy Reasoning Why I chose these numbers

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