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**11**

votes

**5**answers

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

**5**answers

554 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

**1**answer

547 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".
...

**14**

votes

**5**answers

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

**1**answer

217 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 ...