# Tag Info

Accepted

### Rock, Paper, Scissors and Trump

Looks like One strategy would be to The opponent will naturally soon realise what's happening. But it won't help. Here are the possible results from Alicia's point of view: So whatever the ...
• 77.9k
Accepted

### Any fans of The Big Bang Theory?

The key to solving this question is noticing This is a hint to what the dartboard actually represents: So the scoring is given by
• 148k
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• 976
Accepted

### Making a 9 digit number divisible by 11

Note: This answer assumes that the non-zero restriction only holds for the first move, not for any subsequent digits, i.e. that the restriction was imposed only to ensure a valid 9-digit number was ...
• 53.9k

### Finding digits that sum to 15

The solution: The reason:
• 148k
Accepted

• 15.4k
Accepted

### Polynomial game with Devil

It is always possible for you to force the polynomial to have the root $-2$: $$x^2 + (a+2) x + 2a = (x+2)(x+a)$$ Your strategy is to increase your term until it is slightly higher than half the ...
• 7,518

### A Tic-Tac-Toe type game

Another strategy for that works for any odd number of squares:
• 21.8k
Accepted

• 1,704
Accepted

### It'd be on an infinite board, but he can't fit one in his hideout

The winning strategy is and in fact,
• 148k

### The 100 soldier problem

I'll kick off with some observations. Determining a Nash Equilibrium for such a large solution space is not trivial. So here are some numerical attempts for much simpler problems: For problem a, it ...
• 23.7k
Accepted

### 99 numbers on the blackboard

I believe this is the answer. The strategy is below. Edit: Slightly clearer response with strategy.
• 1,016
Accepted

### Noughts and Crosses puzzle

The position is as follows: No two of Eques's counters occupy the same line of 3 (satisfying the never-threatening requirement), and no matter where Knott (O) places their next O, Eques (X) has a ...
• 146k
Accepted

### Blindfold Tic-Tac-Toe

You can't do this going second: The strategy going first is: Interestingly,
• 148k
Accepted

### Catching a Cat on an infinite Line

This is a (semi)infinite version of the Princess in the Castle problem, which is also often asked using a fox or bunny in a row of holes. Infinite is hard to deal with, so lets make it somewhat finite ...
• 53.9k

• 27.4k
Accepted

### A Tic-Tac-Toe type game

I think the answer is that the Strategy
• 138k
Accepted

I'd Then Then So
• 15.9k
Accepted

### Reverse dots and boxes

I would suggest an alternate (simpler) strategy:
• 950
Accepted

### Masyu-making game

Up to symmetries of the board, there aren't very many possible moves for the first player: Does this strategy work?
• 148k

### The Game of Barranca

I'll address whether values of N exist such that if the target of the game is N, there is a winning strategy for the second player[.] The answer is First, a lemma: This seems straightforward ...
• 12.9k

### Making a 2n-digit number divisible by 9

I believe that Bob can win if (and only if) n is
• 8,590

### Clear board in Othello (Generalisation)

Here is one way you could begin to prove that the board can be cleared for all values of $m$ and $n$. Proof by induction. [incomplete] Case 1: $k = 1$ Here we take k = 1 to mean the smallest ...
• 1,018

### 25 square puzzle

Here is another simpler proof This generalises to all odd n. For even n, however, ...
• 53.9k

### Spider and fly on a cube

I think Oray got the right answer. Here are some drawings to illustrate the solution.
• 53.9k
Accepted

• 21.3k

### Who wins this game?

How about this: This method works for $n > 2^k$.
• 4,542
Accepted

### A search game with 2016 numbers

It can be done in: For our questions we use questions similar to those from Ivo Becker's answer: Proof:
• 156
Solution Step-by-step deduction If A plays first, then Proof: the crucial realisation is that B can always force A to play in a specific square. WLOG, say A's first move is an $X$. If A's first ...