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 ...

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17
votes
1answer
676 views

Why are these geometric problems so hard?

I was surprised to learn that both for the Moving Sofa Problem and Packing 11 Squares solutions have been proposed, but in either case the optimality of the proposed solution is, as of yet, only ...
17
votes
5answers
1k views

Lower bound in algorithmic puzzle

Puzzle: there are $n$ computers most of which are good; the others may be bad ("most" in the strict sense: there are strictly more good computers than bad ones). You may ask any computer $A$ about the ...
17
votes
6answers
2k views

Tiling pentominoes into a 5x5x5 cube

I have this wooden puzzle composed of 25 y-shaped pentominoes, where the objective is to assemble them into a 5x5x5 cube. After spending quite a few hours unsuccessfully trying to solve the puzzle, I ...
17
votes
3answers
399 views

Making $121$ with five $0$s

So I say this puzzle online a few days ago and found it quite interesting. The original question was Make $120$ using only five $0$s. Well, I said to myself, this is utterly trivial. Note that ...
17
votes
1answer
2k views

New Year's eve riddle

A bit more than 20 years ago, the following exercise was assigned to a class as the christmas holiday exercise. I did search for a while whether it was posted here earlier and could not find it. I ...
16
votes
2answers
2k views

Interview puzzle with a deck of cards, some cards upside-down

You are sitting in a dark room. It is completely dark. You can't see anything and there is no way that you can make light. Basically, just assume that you are blind for this task. There is a table in ...
16
votes
2answers
982 views

What is the complexity of succinct (binary) Nurikabe?

Nurikabe is a constraint-based grid-filling puzzle, loosely similar to Minesweeper/Nonograms; numbers are placed on a grid to be filled with on/off values for each cell, with each number indicating a ...
15
votes
9answers
460 views

Understanding the solution of a riddle about lions and sheep.

I heard a riddle once, which goes like this: There are N lions and 1 sheep in a field. All the lions really want to eat the sheep, but the problem is that if a lion eats a sheep, it becomes a sheep. ...
15
votes
3answers
2k views

Expanding and understanding the poison pills riddle

You might have heard of the riddle that asks you to identify one fake pill (poisoned) among 12 pills of identical appearance, with the fake pill being either lighter or heavier than the others. You ...
15
votes
2answers
391 views

A “What's my vector?” game

Alice chooses a binary vector $V$ of length $n$ which is unknown to Bob. In each round Bob can choose any number of indices $i$ and then Alice tells Bob how many of the $V_i$ are set to $1$. The ...
14
votes
4answers
6k views

How is this a number sequence 58, 26, 16, 14, 10

I recently had a IQ Test taken and we all got stuck on the same question. The question was: What comes next in the following sequence? 58, 26, 16, 14, _ The answer given in the answer sheet was 10. ...
14
votes
2answers
771 views

Puzzle: $(\Box @)+(\Box @) = (\Box\bigstar\Box$)

Some ETs follow a positional number system, with the same base as the number of fingers on their hand. The following inscription is all the evidence we have: $$(\Box @)+(\Box @) = \Box\bigstar\Box ...
14
votes
3answers
735 views

Puzzle: digit $x$ appears $y$ times on this piece of paper…

There are ten questions on a piece of paper. Your task is to fill in each blank with a positive integer less than 10 such that there is no contradiction. You can reuse any digit. The question is as ...
14
votes
3answers
985 views

Cutting a unit square into smaller squares

My algebra professor gave me this puzzle a while back. I'm pretty sure I've found the right solution; nonetheless, I wanted to share it and see if you come up with anything really nice or unexpected. ...
14
votes
2answers
786 views

Minimally inconsistent Sudoku puzzle

A sudoku puzzle is a partially filled $9\times 9$ grid with numbers $1,\ldots,9$ such that each column, each row, and each of the nine 3×3 sub-grids that compose the grid does not contain two of the ...
14
votes
5answers
1k views

Four men, hats and probability

I encountered the four men in hats puzzle for the first time today. My question is about a realisation I (think I) had while arriving at the solution, but I have no idea whether I've made a mistake ...
14
votes
1answer
307 views

How many strategies are there for this puzzle where one of n logicians must call his own hat's color among n?

$n$ logicians are wearing hats which can be of $n$ different colors. Each logician can see the colors of all hats except his own. The logicians must simultaneously call out a color; they win if at ...
13
votes
6answers
2k views

A strange puzzle having two possible solutions

A friend of mine asked me the following question: Suppose you have a basket in which there is a coin. The coin is marked with the number one. At noon less one minute, someone takes the coin ...
13
votes
4answers
560 views

How to efficiently generate five numbers that add to one?

I have access to a random number generator that generates numbers from 0 to 1. Using this, I want to find five random numbers that add up to 1. How can I do this using the smallest number of steps ...
13
votes
3answers
730 views

The Math behind rotation puzzles?

In the game Machinarium, there is the following puzzle where the goal is to get all of the green points on the green area by rotating them along any of the 3 circles engraved on the background plate. ...
13
votes
2answers
225 views

Another polynomial game

I came across the following problem and I'm stumped. Players X and Y play the following game. For $n\geq 2$, they consider a monic polynomial with degree $2n$, with undetermined coefficients ...
13
votes
1answer
2k views

Is the game 2048 always solveable?

Games got me on math. I always want to play best. I don't know how to answer my question. My question is : How to show that the game 2048 is (always) solvable>? Is there any method other than ...
12
votes
3answers
2k views

What is the mathematical explanation for this trick?

I found the following method to find one's age. It is working exactly for my case. I like to understand and solve this puzzle. If this is wrong forum, my sincere apologies. Please guide me solve this. ...
12
votes
4answers
645 views

expected value of a sum of a 10 sided die

Suppose you have a fair die with 10 sides with numbers from 1 to 10. You roll the die and take the sum until the sum is greater than 100. What is the expected value of this sum?
12
votes
4answers
962 views

A logic problem. No need for calculation

Three people were told to go to a cave and each pick up a hat in pitch dark. The three then came out of the cave with the hat on their heads. There were five hats in the cave. Three of them are black, ...
12
votes
3answers
1k views

evaluate the last digit of $7^{7^{7^{7^{7}}}}$

I found this puzzle online. Since I'm not good at number theoretic kind of problems I'm going to propose it in this form. If you have a number $x$, in this case $x=7$, how do you evaluate the last ...
12
votes
1answer
369 views

Is the solution to this holiday puzzle unique?

I read the following question on this site: Start at 2011. By moving through the maze and doing any arithmetic operations you encounter, exit the maze with a result of 2012. You may pass through an ...
12
votes
2answers
699 views

9 pirates have to divide 1000 coins…

A band of 9 pirates have just finished their latest conquest - looting, killing and sinking a ship. The loot amounts to 1000 gold coins. Arriving on a deserted island, they now have to split up the ...
12
votes
1answer
161 views

Coloring 5 Largest Numbers in Each Row and Column Yields at Least 25 Double-Colored Numbers

This is a question from a very old American Mathematical Monthly, if I recall correctly. It has a very nice solution and illustrates an often useful technique. If it is unsolved after a while, I will ...
12
votes
0answers
216 views

The Right Triangle Game

I am looking for a deeper understanding, particularly the optimum strategy and the maximum score as a function of grid size, of the following (single-player) game played with an $n$ by $m$ grid: ($6 ...
11
votes
11answers
1k views

A proportionality puzzle

My professor gave us this problem. In a foreign country, half of 5 is 3. Based on that same proportion, what's one-third of 10? I removed my try because it's wrong.
11
votes
3answers
783 views

Covering ten dots on a table with ten equal-sized coins: explanation of proof

Note: This question has been posted on StackOverflow. I have moved it here because: I am curious about the answer The OP has not shown any interest in moving it himself In the Communications of ...
11
votes
4answers
1k views

sangaku - a geometrical puzzle

Find the radius of the circles if the size of the larger square is 1x1. Enjoy! (read about the origin of sangaku)
11
votes
2answers
2k views

Enigma : of Wizards, Dwarves and Hats

I've got quite a hard enigma that require extensive knowledge in mathematics, and I thought some might appreciate it. An evil sorcerer holds in prison an infinite number of dwarves (countably ...
11
votes
1answer
923 views

4 by 4 Matrix Puzzle

I was solving the puzzle for the Company interview exam. I found this puzzle, I cannot come up with the solution. How to solve it and what is the correct answer? Determine the number of $4\times ...
11
votes
1answer
1k views

The Three Princesses

Is it possible to solve this problem: A prince wish to marry a princess. There are 3 princesses, one is young, one is a little older and one is old. The prince is able to tell the princesses apart. ...
11
votes
6answers
301 views

When two voters meet, they switch allegiance; might they all ally with the same candidate?

Let's assume that there are three candidates running in an election. Right before the elections (when there is no more propaganda), it is forbidden to gather in groups of more than two people ...
11
votes
2answers
388 views

Packing disjoint family of discs with radii $\tfrac{1}{2}, \tfrac{1}{3}, \tfrac{1}{4},\ldots$ inside the unit disc

Does there exist a family of discs $\lbrace D_{n}\rbrace_{n=1}^{\infty}$ in the Euclidean plane such that the radius of $D_{n}$ is $\frac{1}{n+1}$, each $D_{n}$ is contained in the unit disc, and ...
11
votes
3answers
652 views

Two seemingly unrelated puzzles have very similar solutions; what's the connection?

I think it's an interesting coincidence that the locker puzzle and this puzzle about duplicate array entries (see problem 6b) have such similar solutions. Spoiler alert! Don't read on if you want to ...
11
votes
1answer
316 views

Additive functional inequality

The function $f:R_+\to R_+$ is continuously differentiable and increasing. Also, $f(0)=0$ and $f(\infty)=\infty$. Continuity and differentiability of higher orders can be assumed if necessary. ...
11
votes
1answer
688 views

Given a set of digits, what is the biggest number we can make using exponentiation - numberphile noodle quiz

The question is motivated by a question on a can of number noodles. Each item is a digit between $0$ and $9$. Clearly, if you form a string and consider it to represent a base $10$ integer, then ...
11
votes
3answers
234 views

Deducing correct answers from multiple choice exams

I am looking for an algorithmic way to solve the following problem. Problem Say we are given a multiple choice test with 100 questions, 4 answers per question (exactly one of those four being ...
11
votes
1answer
177 views

How can one determine the chess configuration that maximizes the number of possible moves?

To clarify, what is the chess-board configuration that would maximize the number of valid moves one player could make on his or her turn? I thought of this question while playing chess, how apropos. I ...
10
votes
3answers
962 views

Coffee Break Riddle [closed]

Here's a little brain teaser, for your coffe break: $$ 62-63 = 1 $$ Move only one digit to make it right! Have fun!
10
votes
4answers
1k views

Ten soldiers puzzle

This is a puzzle from one popular book called "The Man Who Counted: A Collection of Mathematical Adventures",author is Malba Tahan. How to arrange ten soldiers in five lines in such a way that each ...
10
votes
3answers
359 views

What is the least amount of questions to find out the number that a person is thinking between 1 to 1000 when they are allowed to lie at most once

A person is thinking of a number between 1 and 1000. What is the least number of yes/no questions that we can ask and know what that person's number is given that the person is allowed to lie on at ...
10
votes
1answer
1k views

After swapping the positions of the hour and the minute hand, when will a clock still give a valid time?

At 12 o'clock, the hour hand and minute hand of the clock can be swapped, and the clock still gives the same time, but at 6 o'clock, it can not be swapped. So in what cases when we swap the hour and ...
10
votes
4answers
2k views

Minimum number of steps needed to solve a rubik cube

Long time ago I've seen a book on group theory and there was an appendix about rubik cube. I remember there were only three steps that enabled me to solve my cube (three strings with letters encoding ...
10
votes
2answers
633 views

How many ways can we let people into a movie theater if they only have half-dollars and dollars?

My interest in combinatorics was recently sparked when I read about the many things that the Catalan numbers count, as found by Richard Stanley. I picked up a copy of Brualdi's Combinatorics, and ...
10
votes
2answers
1k views

A riddle about guessing hat colours (which is not among the commonly known ones)

This is a riddle I heard recently, and my question is if someone happens to know the solution. I'm asking this out of curiosity more than anything else. So here it is. The riddle is one of the ...