# 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.

2,298 questions
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### Uniqueness of spanning tree on a grid.

When I was at the Graduate Student Combinatorics Conference earlier this month, someone introduced me to a puzzle game called Noodles!. The game starts with a collection of "pipes" on a grid (...
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### “Align” ring squares to a uniform color

A ring of N squares, the N is a multiple of 3. "K" squares in the ring are painted of white, and the other squares are painted black. We have a SWITCH operator, that turns the color of 3 adjacent ...
1k views

### Calculating Total Amount of Money Based on Weight

Dealing with US Dollars... Assuming we know the weights of half-dollars, quarters, dimes, nickels, and pennies. Also assuming the weights remain constant (don't change from one quarter to another ...
293 views

### Rosenfeld's $7 \times 7$ square puzzle

A $7 \times 7$ square puzzle may be described as following. Start with a $7 \times 7$ square divided into $7 \cdot 7$ unit squares. First select a unit square and mark it. And then, in each ...
43 views

### Minimum number of dominoes on an $n \times n$ chessboard to prevent placement of another domino.

OEIS sequence A280984 (based on this Math Stack Exchange question) describes the minimum number of dominoes on an $n \times n$ chessboard to prevent placement of another domino. The sequence ...
44 views

### Knights and Knaves problem from Smullyan’s “Logical Labyrinths”

I’d spent a considerable amount of time on this problem before I finally gave up and looked at the solution, where I discovered essentially the deductions identical to mine. In the solution the ...
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### Finding the maximum relative misalignment of numbered rings on a combination lock?

I've been trying to figure out a general formula to calculate the maximum relative misalignment of m identical rings with n symbols each on a combination lock like the one shown below. By "maximum ...
63 views

### $3$ scorpions are chasing $1$ ant on the edges of a cube. The ant is $3$ times faster than any scorpion. Can the ant survive?

The problem: Three scorpions are chasing a single ant on the edgegraph of a cube. The scorpions have the same speed ($v$), while the ant is $3$ times faster ($3v$). They can move in any direction and ...
64 views

### Two friends have $2$ natural written on their forehead. One is $2$ times the other + $1$. They can raise their hands.

The problem: Two friends have $2$ natural written on their forehead. One of them is $2$ times the other + $1$. Let's call them $X$ and $2X + 1$. They have to come up with a strategy to guess their ...
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### Generating all possible Domino tilings on a $4 \times 4$ grid

I have a task to write a program which generates all possible combinations of tiling domino on a $4 \times 4$ grid. I have found many articles about tilings, but it is for me quite difficult and I ...
332 views

### What is special about square numbers here? [duplicate]

I'm not not schooled in math. I'm 50 years old and I only have about a grade 8 level. But I do enjoy math and heard a question in the show "Growing Pains of a Teenage Genius" that interested me. So ...
483 views

### Word Problem Proof? (just for fun, help)

Players $1, 2, 3,\dots, n$ are seated around a table and each has a single penny. Player 1 passes a penny to Player 2, who then passes two pennies to Player 3. Player 3 then passes one penny to Player ...
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### Find the heaviest ball if one weighing can be wrong.

There are 10 ball of some (can be not the same) weights, we need to find the heaviest one, but no more than one weighing can be wrong. I think that we need 19 weighings. We will weigh two balls twice ...
53 views

### Is it possible to send a suitcase with an illegal measurements inside legal one

The airport allows sending a suitcase if the sum of its length, width and height does not exceed a certain constant. Question: Is it possible to send a suitcase with an illegal measurements by ...
114 views

### Minimal number of questions to identify a subset

This is a curiosity question. Recently I stumbled across the following problem : Given three integers $k,m, n$ such that $m+k\leq n$. A friend chooses a subset $S\subseteq\lbrace1,\ldots,N\rbrace$...
55 views

### “Human Knot” solvability probability

Somewhat surprisingly, I don't see a question about this. There is a team-building (or just fun mathematical) game where a group of people hold hands with each other, usually trying not to hold hands ...
371 views

### Dynamic Programming: Largest Number of Dams that can be built

Because of the recent droughts, $N$ proposals have been made to dam the Murray river. The $i$-th proposal asks to place a dam $x_i$ meters from the head of the river (i.e., from the source of the ...
54 views

### Knights and knaves on a square grid

Today Gathering For Gardner posted a video by Yoshiyuki Kotani called "Liar/Truth Teller Patterns on Square Planes". The idea is that you fill a grid with knights and knaves so that both the knights ...
239 views

### Removing points from a triangular array without losing information

I'm trying to find insights about the following puzzle, to see if I can find it on the OEIS (and add it if it's not already there): Suppose I give you a triangular array of light bulbs with side ...
57 views

### Cover a chessboard

Let $2n\times 2n$ board. I cover it with dominoes $1\times 2$ s.t. every cell is adjacent exactly one cell coverd by a domino. I have to find the maximal number of dominoes that can be placed in ...
32 views

### Generalizing this flashlight puzzle

My friend told me a riddle yesterday: four people want to cross a bridge. They each will take $1$, $2$, $5$, and $10$ minutes respectively to cross the bridge. They can go across the bridge in groups ...
117 views

### Let consider a square $10$x$10$ and write in the every unit square the numbers from $1$ to $100$

Let consider a square $10\times 10$ and write in the every unit square the numbers from $1$ to $100$ such that every two consecutive numbers are in squares ...
55 views

### Is the aim of this Swap puzzle possible to achieve?

I have created the following puzzle for the Puzzling Stack Exchange and I need to know if the aim of this puzzle is possible to achieve, hence why I have firstly posted it here. I hope it is not off-...
61 views

### Dudeney’s solutions to haberdasher's problem exact measures of sections

What is the IG length if the side of the square is 1? I wonder if it is half of the square side. The triangle below represents the haberdasher's problem. version 2 version 1 (added after edit, here ...
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### Find the number of the house [duplicate]

A certain street has between 50 and 500 houses in a row, numbered 1, 2, 3, 4, … consecutively. There is a certain house on the street such that the sum of all the house numbers to the left side of it ...
63 views