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18 votes
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 ...
Jaap Scherphuis's user avatar
11 votes

Keys and Locks Puzzle

I believe the condition is: This condition is sufficient. Is this condition necessary?
Florian F's user avatar
  • 30.6k
10 votes
Accepted

Prisoners and warden game, again?

As a brief example of the basic strategy: For the "advanced" strategy:
kagami's user avatar
  • 379
10 votes
Accepted

More Catching of Cats

Let's summarize Jaap Scherphuis's answer to the easier version of the problem where the cat can only move 1 step at a time: Now, since in this version the cat has a step size of $k$, we have to ...
Carmeister's user avatar
  • 2,547
8 votes

Catching a Cat on an infinite Line

Nobody has yet answered the final question, which is the most interesting part... The cat can circumvent capture on any graph with a doubly-infinite chain or a cycle of length at least 3 or size-3 ...
user21820's user avatar
  • 1,236
8 votes
Accepted

Keys and Locks Puzzle

The exact condition is Actually, something slightly stronger is true: A strategy is winning if and only if We can prove this equivalence by an application of Suppose we are handed any strategy. ...
Tim Seifert's user avatar
  • 1,893
7 votes

The Room Of Tiles

I'll say that tile A "beeps" tile B if stepping on A first and then B produces a beep. If we need to be perfectly confident that our choice is safe: If we need a strategy to escape with ...
kagami's user avatar
  • 379
6 votes

Prisoners and warden game, again?

Retudin's user avatar
  • 9,278
4 votes
Accepted

Communicate square on a 3-by-3 grid by flipping precisely one of 13 coins

We have 13 coin positions, which I'm going to give the following names (it doesn't matter which position is given which name, it can be selected arbitrarily as long as I and my ally agree on the ...
ais523's user avatar
  • 2,094
4 votes

Keys and Locks Puzzle

I thought of it in terms of a Suppose Can this always be done?
Tyler Seacrest's user avatar
4 votes

Catching a Cat on an infinite Line

First, let's simplify the problem. Suppose that The puzzle would then be easy to solve: To solve the actual puzzle, we just need to
Jujustum's user avatar
  • 3,957
4 votes
Accepted

Guess the Permutation

Somewhat surprisingly there is a relatively simple method that does not identify 1 until the very end.
Albert.Lang's user avatar
  • 6,195
3 votes

How fast can you win this (very stupid) game?

Here is a table of how many turns it takes for player 2 to win (-1 if player 1 can draw): ...
causative's user avatar
  • 161
3 votes

How fast can you win this (very stupid) game?

Lets start the ball rolling with some examples. k=1, N <= 1 : P1 can draw. P1 can draw by playing m1 = N. P2 has to match that to avoid instant loss. Both have run out of money so game is a draw. ...
Penguino's user avatar
  • 14k
2 votes

Guess the Permutation

A bit of terminology: $p = 2$ $p = 3$ Partial answer for $p \ge 5$ The following strategy almost works, but uses exactly $p$ questions in the worst case. Step 1: Step 1, case 1: Step 1, case 2: ...
Bubbler's user avatar
  • 15.6k
2 votes

Guess the Permutation

Disclaimer: $p>3$ is very closely inspired by @Albert.Lang's solution. The $p=2,3$ solutions are just rehashes of @Bubbler's. This can be Community Wiki if appropriate. Imagine a row of $p$ boxes ...
Benjamin Wang's user avatar
1 vote

Prisoners and warden game, again?

I can almost prove that a lower bound is Conditional on this statement which is reasonable, but I have not been able to prove: If that statement is assumed, we can renumber if necessary so that It ...
Nitrodon's user avatar
  • 289
1 vote
Accepted

Rats & Snakes: Avoid being eaten, escape unharmed

I suspect I'm missing something, as this seems too simple, but the following works for the puzzle as written:
fljx's user avatar
  • 16.6k

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