## How many inclusion preserving maps of subsets?

Let S be a set with n elements and Σk={R⊆S∣|R|=k}. For k≤n/2 how many bijections f are there between Σk and Σn−k, such that x⊆f(x)? For k=1 clearly the answer is the number of derangements of order n. I’m really mostly curious about the case n=2k+1, and even then I would just be happy with … Read more

## Origin of Fujimura set

If we have 10 coins arranged in an equilateral triangle and we want to know the minimum number of coins we can remove so that none of the remaining coins form an equilateral triangle the remaining coins form a Fujimura set. See here for more on this problem. We have been looking at these sets … Read more

## What is God’s number for the WrapSlide puzzle?

WrapSlide is a slide-puzzle (reminding of Rubik’s Cube) consisting of a 6×6 grid of coloured tiles which are separated into four quadrants of 3×3 tiles. When it is unmixed all the tiles in a quadrant have the same colour. A move consists of sliding either the top, bottom, left or right two quadrants of tiles … Read more

## coin reversal puzzle with one hand and two stacks

Suppose that you have N labeled coins pinched in one stack in your fingertips (your palm is above your fingers and your palm is facing down, so that you can drop as many coins as needed from the bottom of the stack) and you have a table which only allows for two other stacks (call … Read more

## A simple language and systematic computations

The following somewhat popular simple computer language was enjoyed on sci.math, sci.math.research, pl.sci.matematyka, and perhaps before and after at several places (I wish I knew it’s exact history). Call this language   SL. An SL-program is a finite sequence of lines, enumerated from   0   to   n−1,   where   n=1 2 …  is an … Read more

## Separating Heavier from the Lighter Balls

This Question was originally posted Here, where I’m more interested in the methods for manual solutions yielding $n$ or less moves on average. I wanted to post it here as well, to see what the people of mathoverflow think about it. I think we are familiar with the classic problem where we need to find … Read more

## Infinite blue eyed islanders puzzle

Can the well known blue eyed islanders puzzle be extended to an infinite number of islanders? In that puzzle, a set of k islanders, each with either blue eyes or non-blue eyes, each knows the color of every other islander’s eyes but not his own. At time t=0,1,… an islander who knows the color of … Read more

## Ulam spiral coordinate system [closed]

Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for MathOverflow. Closed 8 years ago. Improve this question Inspired by a Project Euler problem, I recently started playing around with Ulam spirals. My first thought was that an Ulam spiral could be … Read more

## Reconstruction puzzles

[Added: This is a follow-up of an earlier post.] Consider the following “reconstruction puzzle”, stated informally: Given a concrete poset, e.g. the poset of undirected unlabeled finite graphs without isolated vertices, ordered by embeddability (arrow heads, identities and composition omitted in the diagram):      (source) Now forget about the inner structure of the objects and … Read more

## Guessing the number of other $1$’s in a binary sequence

I have posed the following question on math.stackexchange.com but have not received an answer. So I would like to seek experts’ opinion here. Consider the set of all binary sequence of length $n+1$, $B=\big\{(b_i)_{i=0}^n\,\big| b_i\in\{0,1\}, \forall i\big\}$. Construct a function $f: \{0,\cdots,n\}\times \{0,1\}\to \{0,\cdots, n\}$, such that $\forall (b_i)_{i=0}^n\in B,\,\exists i \colon f(i,b_i)=\sum_{j\ne i}b_j$. What … Read more