Search Results

Motivation. Suppose we are given $6$ boxes, arranged in the following manner: $$\left[\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}\right]$$ Two of these boxes contain a present, and the rem …

Motivation. Recently I stayed at a hotel which had the curious custom to ask their $n$ parties (group of guests, most parties a married couple) which of the $n$ tables they wanted to take. Of course t …

Motivation. My friend works in an organization that is re-organizing itself in the following somewhat laborious way: There are $n$ people currently sitting on $n$ jobs in total (everyone has one job). …

Motivation. With my younger son I played the following game on a big (dysfunctional) clock which can be modelled as $\mathbb{Z}/12\mathbb{Z}$ : Put the clock hands at number $12 ( = 0)$. Toss a coin, …

The following is inspired from the most recent riddle of the week of the German news magazine Der Spiegel. For any positive integer $n\in\mathbb{N}$, let $[n]$ denote the set $\{1,\ldots,n\}$. Let $E_ …

Real life motivation. In my younger son's class, there are $18$ students. His teacher provided $18$ time slots for the parents of each child to have a 30-minute conversation of their kid's progress in …

"Real-life" motivation. The German satirical magazine Der Postillon suggested a few measures for deterring smokers from their bad habit. I especially liked the idea of inserting one "prank cigarette" …

Fix a positive integer $n$. Every second, a particle is sent along a straight line from a fixed position in a fixed direction, at a random integer speed chosen uniformly in $\{1,\ldots, n\}$ meters pe …

Motivation. Swiss license plates consist of $2$ letters indicating the region, followed by a number, such that the pairing (region, number) is unique by car. In the small town where I live, I saw two …

Motivation. In a coin game, a player flips all their coins every turn, starting with just one coin. If the coins all land heads then the game stops; otherwise, the number of coins is doubled for the f …

We are given an integer $n \geq 1$ and $2n$ cards, labelled $0$ to $2n-1$. We pick a card with uniform probability, put it back, and continue, until for some $k\in \{0,n-1\}$ the cards $2k$ and $2k+1$ …

This is based on an older question. For $n\in\mathbb{N}$, let $[n]:= \{1,\ldots,n\}$. Let $\text{Fun}(n)$ denote the set of all functions $f:[n]\to[n]$. To $f\in\text{Fun}(n)$ and ''starting value'' $ …

For $n\in\mathbb{N}$, let $[n]:= \{1,\ldots,n\}$. Let $\text{Fun}(n)$ denote the set of all functions $f:[n]\to[n]$. To $f\in\text{Fun}(n)$ associate a sequence $\text{seq}(f))$ defined recursively by …

Motivation. As I was playing the pairs-matching game "Memory" (known as "Concentration" in some parts of the world) with my children, I was surprised that even thorough shuffling could not prevent qui …

First, we note that there is a natural bijection ${\cal P}(\omega) \to \{0,1\}^\omega$ and endow the latter with the product topology (where $\{0,1\}$ carries the discrete topology). So we get a compa …