# Tag Info

### Chasing pirates

Stay put for about 45 days, after which the pirates would have circumnavigated the globe and returned to your current position.
• 1,044
Accepted

### How to beat Count Dracula

The lockets and coffins are always found in loops. open a coffin look at the number of the locket in the coffin go to the coffin with the same number as the locket open the coffin repeat from 2 At ...
• 5,846

That's easy
• 2,586
Accepted

### The lion and the zebras

Here is the strategy:   It works because:
• 7,678
Accepted

### Coin Flipping Game with the Devil

Satan should stick to fiddling. You will win, and here is a simple proof. Consider the game $n$ turns at a time. After each cycle of $n$ turns, all the coins are in their original position (though ...
• 7,678
Accepted

### Left coin, right coin, last coin?

It doesn't matter which option you choose, because Your probability of survival if you're one of n players left is as follows: Informal proof It was established in the question that if there are ...
• 114k
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### 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 ...
• 69.3k
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### Chasing pirates

If we assume the ocean is flat and extends indefinitely in all directions, there is a strategy that guarantees we can catch the pirates in at most 800,000 years. Put our current location as the ...
• 13.9k
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### Coins on a table

The winning strategy for the first player is to put their coin in the dead center of the table. Then whatever move their opponent makes, they exactly mirror it, around the center. e.g. If the second ...
• 2,329
Accepted

because:
• 2,819

### Left coin, right coin, last coin?

The answers of rand al'thor and Callidus are great; I just want to give a different argument for the result. Claim: After each round, the number of surviving players is even. Proof: Let $f_i$ be the ...
• 23.7k
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### A lonely pawn on the chessboard

Strategy: How this works:
• 5,846
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 ...
Accepted

### Titanic Tic-Tac-Toe

The first player can always force a win. I wrote this Python script to analyze the tree of possible game states reachable from an empty starting board. No matter what the second player does, the ...
• 6,329

### Finding digits that sum to 15

The solution: The reason:
• 139k
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### Rook game on chessboard

I will assume that the square in the lower left is painted red as well. Note that an $m\times n$ board is the same as an $n \times m$ board. So WLOG we will assume that $n \le m$. When $n=m=1$, ...
• 8,841
Accepted

### Blackboard cleaning

Dr Xorile's answer of is optimal. Suppose that the numbers 1, 2, 4, 8, ... 512, and 1024 are all on the board. In order to eliminate the number $2^i$, there must be some step where you decrease $2^i$...
• 31.5k
Accepted

• 841
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### 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 ...
• 7,333

### A Tic-Tac-Toe type game

Another strategy for that works for any odd number of squares:
• 21.4k
Accepted

### Knight on a 5 by 5 board

As shown below Alice gives the red moves and Bob gives blue moves... Moves 2 and 10 have symmetrical options which end up with same result. All other moves are forced.
Accepted

### Face Up Poker with Alice and Bob

There is a winning strategy for
• 13.9k
Accepted

• 10.2k