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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0
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4answers
92 views

how many words can be formed using all letters in the word EXAMINATION

Assuming any sequence of letters is a word, how many words can we form in such a way that the first two letters are different consonants while the last two letters are vowels?
0
votes
2answers
44 views

Find radius and height

I have the following problem: given the length of the chord AB and the length of the arc AB, find the radius of the circle and the height of the triangle ACB where C is a point on the circle such that ...
1
vote
1answer
42 views

Is it possible to create a bigger square using distinct smaller ones?

Another user just inquired about possible solutions to the famous $70$x$70$ square puzzle. When I encountered that many years ago and the first idea that came to my mind as to why I wouldn't think it ...
0
votes
3answers
74 views

Lightbulb puzzle related to proofs by induction.

The puzzle question was as follows: There is a circle of $n > 2$ lights with a switch next to each of them. Each switch can be flipped between two positions, thereby triggering the on/off states of ...
50
votes
5answers
8k views

Help me solve my father's riddle and get my book back

My father is a mathteacher and as such he regards asking tricky questions and playing mathematical pranks on me once in a while as part of his parental duty. So today before leaving home he sneaked ...
32
votes
6answers
2k views

Fun Geometric Series Puzzle

I recently was reminded of a puzzle I solved in college and thought I'd give it a shot again. However, being distanced from college math, I am having a harder time remembering how I arrived at the ...
-2
votes
1answer
83 views

The “Four beer caps” puzzle [closed]

Four beer caps are placed on the corners of a square table with arbitrary orientations. There is a robot on the table that acts upon three commands: (a) “flip a corner cap”, (b) “flip two diagonal ...
0
votes
0answers
392 views
+100

Fitting Expanding Spheres in the Irregular Surface

This is a kind of a puzzle: I have a convex hull filled with $N$ small spheres(with radius $r$). Now, the balls grow in size till it hit any side of the Cavity (Convex hull) or any other ball. ...
18
votes
2answers
1k views

A riddle with a witch and some gnomes

My question concerns a variation and a generalization of the following riddle. The Original Riddle: A wicked witch kidnaps 2 gnomes. She paralyzes them, and places a hat on each of their heads. Each ...
1
vote
1answer
64 views

Books in mathematics based on problem solving

Hi I'm looking for mathematical books that try to teach mathematical concepts by motivating and solving real life problems. For example a book in topology that is motivated by problems of planetary ...
12
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 ...
8
votes
1answer
82 views
+150

Blocking lines of length $5$ in a $7 \times 8$ matrix; how can we know the solutions have a specific form?

A friend shared with me the following puzzle he encountered in a Chinese math competition: In a $7 \times 8$ matrix, we place tokens so that any straight line of length $5$ (horizontal, vertical, ...
41
votes
15answers
13k views

Interview riddle

On the Mathematics chat we were recently talking about the following problem @Chris'ssis had to solve during an interview : $$3\times 4=8$$ $$4\times 5=50$$ $$5\times 6=30$$ $$6\times 7=49$$ ...
-5
votes
0answers
76 views

Pirates And Coins No.2

this time the assumptions are same as the first question but this time there are six pirates and they have found just one coin the question is: the first pirate what will do?
2
votes
2answers
317 views

Pirates And Coins No.1

I actually like this one: There are five pirates in a ship and they have found 100 coins. The biggest pirate offers a way to divide the coins. If at least half of them agree on the division, it will ...
3
votes
1answer
74 views

Prove that there is only one way to make a square using all six tangram pieces

I am pretty sure there is only one way to make a square from the six tangram pieces: How can I prove this is the only way respecting all symmetries?
1
vote
0answers
21 views

A good book with algorithmic puzzles with solutions (not of kind “how to pass and IT interview”)

can you please advise me a book with algorithmic and mathematical (IT-oriented) puzzles. But I want not one more book of kind "How to pass an interview in Microsoft / Google / any other big company" ...
1
vote
1answer
46 views

How can I write a system of equations puzzle if given the solutions? (work backwards?)

\begin{matrix} a = 12 & b = 6 & c = 5 & d = 1 & e = 0\\ \end{matrix} How can I create a fun puzzle or word problem that would arrive at this solution above? For example, ...
1
vote
1answer
45 views

How to derive the answer for this puzzle problem visually?

I was looking at this problem on Puzzle StackExchange about working out the proportion of sand in two separate beakers. Rather than providing a mathematical explanation, I thought it would be easiest ...
1
vote
2answers
69 views

The defective doyle

There are six cans each containing doyles(each doyle weighs a gram), out them any of them can be defective. How can we find the defective cans in one weighing? and if each can has only two dozen ...
0
votes
2answers
91 views

Advanced Counting Puzzle

Suppose we have a house in which every room has an even number of doors. Prove that the number of doors from the house to the outside world is also even.
5
votes
2answers
59 views

Non-geometric way to calculate expected value of breaks?

In "50 Challenging Problems in Probability", question #43 is the following: "A bar is broken at random in two places. Find the average size of the smallest, of the middle-sized, and of the largest ...
3
votes
6answers
318 views

Puzzle about technique of fair using of unfair coin

There is an unfair coin. It tends to land on one side more than on the other. It is unknown which side is it. There is Mr. A and Mr. B. They argue about something and they want to use that coin to ...
0
votes
2answers
30 views

Puzzle about subjects, classroom numbers and teachers who teach those subjects in classrooms

A,B,C,D,E are teachers who may teach: math, physics, chemistry, biology or geography(one subject per person, we don't know who teaches what). They teach in classrooms 110,111,112,113,114. Tell which ...
2
votes
2answers
70 views

Russian roulette should a player pull the trigger or spin the cylinder

Two men plays Russian roulette. In revolver there are 2 bullets in consecutive chambers( 2 bullets are in 2 chambers next to each other). One man spun the cylinder, pulled the trigger and he is fine, ...
1
vote
1answer
48 views

Find A,B,C,D consecutive numbers based on written addition formula

$A, B, C, D$ are consecutive digits: $B$ is greater by $1$ than $A$, $C$ is greater by $1$ than $B$, $D$ is greater by one than $D$. Four $X$s are digits $A,B,C,D$ in unknown order. Find $A,B,C,D$ ...
0
votes
1answer
65 views

Puzzle about phographers in Africa taking pictures of 2 Animals which name corresponds to last name of their friends

Leo Lion, Tom Tiger, Eddie Elephant, George Gazelle, Peter Panther, Luke Leopard were on photographic safari in Africa. Every photographer took a picture of 2 animals. Every of these 2 animals ...
0
votes
1answer
38 views

Different approaches for this problem (number in different bases)

I came across the following problem on a puzzle website the other day. A $3$ digit number is written $(xyz)_{10}$ in base $10$ and $(zyx)_9$ in base $9$. What is it? The website (which I think ...
0
votes
2answers
64 views

A question from a job interview: math function that returns the number of positive numbers.

Describe a mathemathical function that receives 5 parameters, And returns the number of positive numbers. $f(x_1,x_2,x_3,x_4,x_5)\to 5,4,3,2,1,0$ - according to the number of positive numbers. ...
5
votes
1answer
69 views

Drawing previously undrawn cards from a deck

Suppose you have a deck of $y$ cards. First, randomly select $y-x$ distinct cards and sign the face of each, then shuffle all the cards back in to the deck. Proceed as follows: Draw a card. If it is ...
3
votes
0answers
64 views

A game on a smaller graph

In this question Alice and Bob play a game on $K_{2014}$, Alice directing one edge, Bob directing $1$ to $1000$ edges with Alice trying to make a cycle. The proof that Alice can win depended on the ...
1
vote
4answers
85 views

Probability: A variant of the Monty Hall Problem

Monty has a new game it's like his old one but now there are no goats just one car hiding behind one of three doors and this time he doesn't know where the car is. To play you pick one of the three ...
0
votes
0answers
19 views

The problem category of sudoku Puzzle solved by search algorithms

Good day everybody, Sudoku puzzle solvers have been categorized in the literature to: Deductive algorithms that perceive sudoku as a hard constraint satisfaction problem (CSP) or Boolean ...
1
vote
1answer
81 views

logic\math question [closed]

Hi, This is allegedly a very simple question....most of the people answered that the answer is 9=90. i claim that theoretically, you can't be 100% sure about the right answer because you don't know ...
11
votes
1answer
302 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. ...
1
vote
4answers
87 views

Two children paradox : where is my reasoning wrong?

I hope here is the good place to be asking this. Apologies otherwise. The statement is as follow : "Ms Michu has two children. We know one of the two is a girl, we call that girl Ludivine. What is ...
7
votes
3answers
42 views

Probability Puzzle: Mutating Loaded Die

Take an (initially) fair six-sided die (i.e. $P(x)=\frac{1}{6}$ for $x=1,…,6$) and roll it repeatedly. After each roll, the die becomes loaded for the next roll depending on the number $y$ that was ...
2
votes
1answer
47 views

How Many of a Given Weekday Fall in a Month

A month can have either $31, 30$, or $28$ days excluding leap years. Suppose we want to know "how many Fridays are in a given month". By considering the maximal case where the first Friday falls on ...
3
votes
0answers
102 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 ...
1
vote
1answer
43 views

Largest factor of sum of all 3-digit numbers…

What is the largest number (so, yes, I am looking for a discrete integer not an algebraic expression) by which the sum of all 3-digit numbers formed with the non-zero, distinct digits a, b, and c MUST ...
2
votes
0answers
41 views

Number of tries to guess M-1 letters from M-letters-code.

There are N letters in an alphabet. There is a combination lock, the code to it consists from M different letters. You can input M letters combination to try to open the lock. If you guess at least ...
3
votes
1answer
104 views

When to be sure that we have counted all the squares in such problems [duplicate]

My first question is: How would one solve such problems (in general,squares+rectangles). What should be the general technique?How can this problem be reduced to a mathematical problem? My second ...
1
vote
1answer
65 views

Math Competition Question Hong Kong 2

Note: This is from the Po Leung Kuk 2012 paper. The previous one I posted was from the Po Leung Kuk 2011. Here's another question for everyone: There is a figure made out of two rows of identical ...
2
votes
2answers
66 views

Finding the ball

There are $N$ balls such that out of these balls only one ball is heavier. We have one balance scale. With it we can know which of two ball groups is heavier. Balls get damaged when weighed, so each ...
2
votes
2answers
74 views

Chords of a 20-gon

Twenty points lie on a circle, so as to form a regular polygon. Then they are split into ten pairs, and the points in each pair are connected by a chord. Prove that some pair of these chords have the ...
1
vote
0answers
35 views

Number of solutions to sudoku puzzle

Inspired by this question, consider hints on a Sudoku board. A regular puzzle has a unique solution. It is clear that there are puzzles with 2 or 3 solutions, and therefore, I guess, puzzles with say ...
1
vote
0answers
48 views

R. Jeffrey and the Three Prisoners

Here’s something curious, from p. 26 of the estimable Richard Jeffrey’s last, posthumously-published book, Subjective Probability: The correct (or at least orthodox) answer to this puzzle would be ...
1
vote
1answer
111 views

Prove that it is impossible to make 18

Today, I was shown the following puzzle: Find a way to make the numbers $ 7 $ through $ 18 $ using any three adjacent numbers in the grid below: \begin{array} {|c|c|} \hline 10 & 10 & 9 ...
1
vote
1answer
60 views

Math Puzzle Solving

Using each of the digits 1,2,3,4,5,6,7,8 exactly once fill in the boxes so that no consecutive number is adjacent or cross to ...
2
votes
0answers
71 views

A mathematical game: moving tiles

There is a mathematical game called moving tiles. There are $8$ different movable tiles on a $3 \times 3$ board, At the beginning the tiles' location is given as following: ...