All Questions
32
questions
16
votes
0
answers
714
views
Optimal strategy for guessing a binary string
I would have thought this was well known, but I have not been able to track down a reference.
Suppose you are trying to guess an $n-$digit binary string. At any point you may guess all or any portion ...
- 71.9k
5
votes
1
answer
289
views
Showing that losing positions in Wythoff's game are generated by $(\lfloor n\phi\rfloor, \lfloor n\phi^2\rfloor)$, where $\phi$ is the golden ratio
A very neat problem in combinatorial game theory:
In Wythoff's Game, how do I show that all the losing positions are generated by the formula
$$\left(\lfloor n\phi\rfloor, \lfloor n\phi^2\rfloor\...
- 375
6
votes
1
answer
256
views
Billy and Bob start with two rectangular grid which can be modeled as a chocolate
Billy and Bob start with two rectangular grid which can be modeled as
a chocolate. They take turns cutting and eating the chocolate: on
their turn, they can cut the chocolate along an edge parallel to ...
- 87
16
votes
2
answers
661
views
Infection spread on a torus chessboard
In one of his books, Peter Winkler includes the following problem:
A disease is spreading on a $n\times n$ chessboard as follows: if a healthy cell is neighboring at least 2 infected cells, it becomes ...
- 383
1
vote
0
answers
75
views
$k$ isolated prisoners with hats, $n$ possible hat colors, $k$ tries to guess everyone's color after initial chat before hat assignment
Basic problem:
$2$ prisoners are in a room, they are allowed to chat and come up with a plan for the riddle they are about to face. After their chat, they are separated and assigned one hat each, ...
- 989
1
vote
1
answer
272
views
Optimal moves for maximizing perimeter?
Herman and Alex play a game on a $5 \times 5$ board. On his turn, a player can claim any open square as his territory. Once all the squares are claimed, the winner is the player whose territory has ...
- 141
0
votes
1
answer
278
views
Guess ball colors
7 people receive either a black or a white ball. They can only see the color of the others balls, but not their own. Both of the colors are equally likely. They play as a team a game of guessing their ...
- 719
3
votes
1
answer
1k
views
Looking for solution to "lights out" puzzle variant with multiple states
Recently in World of Warcraft, there is a puzzle that is very similar to the "lights out" puzzle where a player needs to flip switches to turn all the lights into a specific color (in this case yellow,...
- 155
5
votes
1
answer
149
views
Optimizing a winning strategy for a quick tabletop game
A friend of mine recently shared the following puzzle with me:
Puzzle: A circular turntable is divided into four congruent quadrants by two perpendicular lines. (Think of a circle in the $xy$-...
- 22.9k
9
votes
1
answer
1k
views
Identify a truth-teller among a group of truth-tellers and (honest) liars.
This question is inspired by this thread. In that thread, a liar may both tells lies and truths. However, in my version, liars always lie.
Main Question. A group of people consists of $m$ truth-...
- 49.8k
2
votes
1
answer
143
views
Expected profit of my simple board game
How to play:
Use 1 host and at least 1 player
Each player has to toss fair six-sided dice to go to goal.
If the player is at the 35th cell and tosses 2 or more, he can go to goal aa same as he ...
- 725
1
vote
0
answers
281
views
Cyclic Partisan Nim Variant
This game is played with a sequence of heaps and a position marker, where each heap is owned by exactly one player. The game ends when a player has removed all objects from their own heaps, and this ...
- 330
13
votes
3
answers
2k
views
An invisible ghost jumping on a regular hexagon
Given a regular hexagon and an invisible ghost at one of the vertices of the hexagon (we don’t know which). We have a special gun, that can kill ghosts. In a step we are able to shoot the gun twice (i....
- 1,516
29
votes
3
answers
1k
views
Hat 'trick': Can one of them guess right?
There are $n$ boys and $n$ girls. Each of them is given a hat of only 4 possible (known) colors and doesn't know its color. Now each can only see all the colors of hats of those of the other gender ...
- 1,353
3
votes
2
answers
318
views
Binary encryption puzzle
There are 8 rooms, one containing a pot of gold. You know which room the gold is in, but your partner does not. The task is to inform your partner which room the gold is in under the following ...
- 363