# Questions tagged [puzzle]

This tag is meant for questions about the mathematical principles behind games, riddles, or their possible solutions. If the answer is known to you please do not use this tag to "riddle" other users, but rather to ask about the correctness of a possible solution or ways to extend and improve an existing solution.

316 questions
343 views

### Infinite Rubik's Cube

Is there an infinite analog to the Rubik's Cube? What does its solution-algorithm look like? For illustration, consider the Rubik's cube with infinite tiles to a side, on all sides, with sides of ...
2k views

### This should be a piece of cake… right?

You probably know the following problem: We have two circular cakes of the same height but unknown and potentially different radii, and we want to cut them into two equal shares. Each cut can only ...
378 views

### History of a combinatoric problem: exchanging numbers by throwing stones

Another user recently asked a question on the Puzzling stack: Two spies throwing stones into a river. Suitably generalised, it becomes: Two spies (Alice and Bob) need to exchange a message. Each ...
402 views

### How many distinct Unruly boards are there?

Unruly is a puzzle game played on a board of $2n × 2n$ squares. Each square must be colored either black or white, with the following constraints: Each column must have $n$ white squares and $n$ ...
373 views

### $5 \times 5\;$ “square additive set”

Problem: IBM Research - Ponder This - January 2019 monthly contest (which was closed few days ago) leads to the problem: Find sets $A = \{a_1,a_2,\ldots,a_n\}$, $B = \{b_1,b_2,\ldots, b_m\}$ such ...
198 views

### Solving general (dis)entanglement puzzles

What is the state of the art in (modelling and) solving a general (dis)entanglement puzzle? The following picture shows a nice example: There is a project called "The Untangler", which seems to be ...
308 views

### Separating Heavier from the Lighter Balls

This was posted Here and received a good answer, solving the general questions in either $n$ or $n+1$ moves, which is by just half a move on average "less good" than my manual solutions here. Classic ...
231 views

### Limit approximation for $\pi$ in the four fours puzzle?

The four fours puzzle is a recreational math puzzle whose aim is to express whole numbers using four occurrences of the digit 4 and a specified set of operators. A common variety permits the following:...
97 views

### Can this puzzle be solved using the representation theory of quivers?

This riddle originates in the youtube video here. It's mathematical content was summarised here as follows: There's a $5\times 5$ grid of nodes, all nodes are (bidirectionally) connected to their ...
78 views

### Flipping odd number array by two numbers in series.

Suppose an array of length $n$(odd number) which is composed with only $0$. We start to ‘flip’( or ‘change’) numbers with following rules. [1, 1] → [0, 0] [0, 0] → [1, 1] [1, 0] or [0, 1] : do not ...
250 views

### How to prove if an N size jigsaw puzzle is solvable.

Let's say we have a jigsaw puzzle with N pieces. Each piece has 4 sides and can only have one of three fits: a straight fit, a concave fit and convex fit. A side can only fit with another side if both ...
142 views

### Impossible permutations of the Gear Cube

If you're familiar with the group properties of the Rubik's Cube, you will probably know that, under the action of the standard moves, all possible permutations of the (unoriented) edge pieces are ...
134 views

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### Subdividing regular pentagon into six congruent pieces

It is easy to divide a 2-gon into 3 congruent line segments. It is also easy to divide a triangle into 4 smaller triangles that are congruent. One of Martin Gardner's favorite problems is to show that ...
235 views

A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
307 views

### Puzzle - zero knowledge proof

I am solving the following problem : I have edge-matching puzzles, where all pieces are squares and the grid has $n$*$n$ format. There is no global image to guide a puzzle solver. Despite the puzzles ...
172 views

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### Gauss-Jordan elimination on banded matrix $O(n)$ time?

My motivation is solving arbitrary Lights Out puzzles with a method given in MathWorld. Normally Gauss-Jordan elimination takes $O(n^3)$ time, but notice the addition matrix that combines all the "...
151 views

### Find four whole numbers… Is this maths question impossible?

I'm helping out my nephew with his 11+ exam revision. We have practice papers but no answers so. One of the questions is as follows: Find four whole numbers whose sum is 400, such that the first ...
387 views

### A list of math puzzle sites that require little knowledge beyond first year college math, just a lot of creativity?

A while back I found IBM's Ponder This website. http://www.research.ibm.com/haifa/ponderthis/ What is wonderful about that site is that a large number of the problems there don't require advanced ...
213 views

### Extending the general solution to the “Four fours” problem

The four fours puzzle is, given a number $n$, how can you represent $n$ with common (or more specifically, elementary) mathematical functions and 4 or less occurrences of the digit 4. On the ...
200 views

### Candy Crush as an integer programming problem

I'm trying to model the basic version of a match-three game, where the player (has a maximum number of swaps) must swap any two adjacent gems (no diagonals) in an 8x8 grid of gems in order to match ...