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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21
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5answers
5k views

Puzzle of gold coins in the bag

At the end of Probability class, our professor gave us the following puzzle: There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of ...
21
votes
2answers
439 views

Shortest possible unreachable shape

This is a follow up to Is every shape possible with a snake? . Imagine a 2d snake formed by drawing a horizontal line of length $n$. At integer points along its body, this snake can rotate its body ...
21
votes
1answer
455 views

Finding real money on an even stranger weighing device

You have $n$ coins which each weigh either $20$ grams or $10$ grams. Each is labelled from $0$ to $n-1$ so you can tell the coins apart. You have one weighing device as well. At the first turn you ...
21
votes
0answers
425 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 ...
20
votes
10answers
3k views

Get $5$ by doing any operations with four $7$s

How can one combine four sevens with elementary operations to get $5$? For example $$\dfrac{(7+7)\times7}{7}$$ (though that does not equal $5$). I am not able to do this. Can you solve it or prove ...
20
votes
2answers
975 views

Getting $22$ as the answer always

I am puzzled by the below exercise: Step 1: Select any number having 3 digits (all different from one another). Ex. $125$. Step 2: Now, write all possible combination of two digit number forming ...
20
votes
4answers
410 views

How many $\mathbb R$s must a Mathematician walk down?

A mathematician is lost on the complex plane. He knows neither his position nor the direction he is facing. He wants to return to the main road, a strip of width $1$ around the real axis (that is, ...
20
votes
1answer
1k views

The $n$ Immortals problem.

I saw this riddle posted on reddit a long time ago, called the "Seven Immortals." In the beginning, the world is inhabited by seven immortals, ageless and sexless, who begin to multiply and ...
20
votes
3answers
633 views

Math puzzle: 10 digit strings generations

There was a question in a math competition that I attended last year. At the end of competition, I realized that my answer was wrong for the question below and I have never been able to figure out how ...
19
votes
9answers
4k views

Is Lewis Carroll's reasoning correct?

A bag contains 2 counters, as to which nothing is known except that each is either black or white. Ascertain their colours without taking them out of the bag. Carroll's solution: One is black, and ...
19
votes
2answers
599 views

Connecting a $n, n$ point grid

I stumbled across the problem of connecting the points on a $n, n$ grid with a minimal amount of straight lines without lifting the pen. For $n=1, n=2$ it is trivial. For $n=3$ you can find the ...
18
votes
7answers
2k views

“How long 'til we get there?” Road trip puzzle

Road trips can be fun, but they often appear to go slower the closer you get to your destination. I thought up this puzzle while on a recent trip. Thought it would be good food for thought. Curious ...
18
votes
3answers
2k views

Why should Rubik's cube get attention from mathematicians?

I've seen a lot of math debate, calculations and other stuff related to Rubik's cube lately, but I don't really understand why is it important, why should anyone spend time asking and answering ...
18
votes
1answer
848 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 ...
18
votes
2answers
766 views

Puzzle: Cracking the safe [duplicate]

A safe is protected by a four-digit $(0-9)$ combination. The safe only considers the last four digits entered when deciding whether an input matches the passcode. For instance, if I enter the stream ...
18
votes
2answers
397 views

Game involving points on $[0,1]$

You're given a list of $22$ points in $[0,1]$ (not necessarily distinct), and you're asked to select, at every iteration, $2$ points to be substituted by their midpoint. After $20$ iteration, you ...
17
votes
6answers
6k views

Can you complete the expression $2 \underline{ }\, \underline{ }\, \underline{ } \,\underline{ } 5 = 2015$?

Can you complete the expression $2 \underline{ } \, \underline{ }\, \underline{ } \, \underline{ } 5 = 2015$ and make it correct by replacing two underscores with a selection of the ...
17
votes
8answers
3k views

The Three Princesses (distinguishing truth-teller with 1 question)

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. ...
17
votes
3answers
3k views

Largest prime number with all digits different

What is the largest prime with distinct digits? (It is certainly less than ten digits long.Can you explain it why?
17
votes
4answers
4k views

100 prisoners and a lightbulb

100 prisoners are imprisoned in solitary cells. Each cell is windowless and soundproof. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb ...
17
votes
3answers
454 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
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
3k 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
2answers
502 views

Is it true that we can get zero for all $(x,y,z)\in\mathbb{N}^3$?

There are three distinct positive integers $x$, $y$, and $z$. We can choose two numbers $a,b\in\{x,y,z\}$, where $b\leq a$, then replace $b$ by $2b$ and replace $a$ by $a-b$. Is it true that there ...
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
3answers
1k 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!
16
votes
4answers
11k 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. ...
16
votes
2answers
3k 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
931 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 ...
16
votes
3answers
7k 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 ...
16
votes
1answer
486 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 ...
16
votes
1answer
1k 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 ...
16
votes
2answers
544 views

The Weaver Android app $\rightarrow$ cute combinatorics problem

There's an Android puzzle app called "The Weaver". My question is why every level seems to be solvable in far fewer moves than one might naively think. Here's a link for people who want to play along ...
16
votes
2answers
1k 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 ...
16
votes
0answers
263 views

What Rubik's Twist configuration has the lowest visible surface area?

The Rubik's Twist has been a fun time sink. From the wiki page, [It] is a toy with twenty-four wedges that are right isosceles triangular prisms. The wedges are connected by spring bolts, so that ...
15
votes
2answers
867 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 ...
15
votes
3answers
817 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 ...
15
votes
3answers
888 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 ...
15
votes
4answers
2k views

Solving 9 sons puzzle

The following math puzzle : ...
15
votes
8answers
2k 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
417 views

Is it possible to uniquely number faces of a hexagonal grid with consecutive numbers?

You have a grid of regular hexagons. The aim of the game is to have each hex contain the numbers 1-6 on its edges. Each edge must also be connected to another edge that has a value one higher and ...
15
votes
2answers
425 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
3answers
1k 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
5answers
3k 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
2answers
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 ...
13
votes
3answers
4k 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. ...
13
votes
4answers
1k 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?
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
593 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
1answer
403 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 ...