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11
votes
5answers
3k views

Guess a number with at most one wrong answer

Consider a game where one player picks an integer number between 1 and 1000 and other has to guess it asking yes/no questions. If the second player always gives correct answers than it's clear that ...
19
votes
5answers
547 views

$n$-in-a-row game on $\mathbb{R}^2$

For integers $n$ such that $\:3< n\:$,$\:$ what is known about the following 2-player game: Player_1 and Player_2 take turn choosing points on $\mathbb{R}^2$ that were not previously chosen, with ...
15
votes
1answer
510 views

Paul Erdős: Determine or estimate the number of maximal triangle-free graphs on n vertices

Among the collections of the open problems of Paul Erdős on the website of Professor Fan Chung, there is one called "number of triangle-free graphs". ...
13
votes
5answers
2k views

Irreversible chess

Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no ...
7
votes
1answer
216 views

Optimum Tournament Strategy

Consider a symmetric N-player game in which all players partition one total unit of energy among individual games. The probability of winning each game is simply proportional to the spent energy ...