# Tag Info

1

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 ...

11

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

4

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 ...

2

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

10

The player who can win is by this strategy:

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First player wins Example:

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

14

I would suggest an alternate (simpler) strategy:

0

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

5

The player with the winning strategy is Strategy

3

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

2

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 ...

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

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