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

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

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