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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11
votes
2answers
232 views
+200

Finding real money on a strange weighing device

You have 50 coins which each weigh either 20 grams or 10 grams. Each is labelled from 0 to 49 so you can tell the coins apart. You have one weighing device as well. At the first turn you can put as ...
2
votes
0answers
16 views

Puzzle: Determining the structure of a bipartite graph

Consider the bipartite graph $G = (X, Y, E)$, with $|X| = |Y| = n$. We can think of $X$ and $Y$ as clusters of $n$ switches on either end of a long hallway. Each switch on one end of the hallway has ...
5
votes
3answers
86 views

Number of ways through a modified grid

I was in math class listening to my teacher blather on about solids of revolution when my friend passed me a note with a puzzle on it. It looked something like this: How many different ways can you ...
-3
votes
2answers
65 views

Can I divide $50$ cars on$ 5$ days? any trick? [on hold]

Can I divide $50$ cars on $5$ days, on condition that the numbers should be prime numbers? is there any trick? I'm asking for $5$ prime numbers whose sum is $50$
2
votes
1answer
64 views

A math puzzle about slow clock

You have the misfortune to own an unreliable clock. This one loses exactly 20 minutes every hour. It is now showing 4:00am and you know that is was correct at midnight, when you set it. The clock ...
4
votes
2answers
559 views

Puzzle on the triangle.

In triangle top four figures that have to be repositioned to form the "triangle" without a unit square. How to explain this? Thank's.
2
votes
2answers
784 views

Seating Arrangement puzzle.

Not sure if its a correct place to post these kind of questions. Eight persons-P,S,Q,R,U,B,J and C are sitting in a field in a circle. Three are facing opposite side and other five are facing the ...
1
vote
0answers
98 views

Maths puzzle 1: smart play with sets

Let $$X=\{ a, b, c, d, e, f, {ab}, {ac}, {ad}, {ae}, {af}, {bc}, {bd}, {be}, {bf}, {cd}, {ce}, {cf}, {de}, {df}, {ef}, {abc}, {abd}, {abe}, {abf}, {acd}, {ace}, {acf}, {ade}, {adf}, {aef}, {bcd}, ...
-5
votes
4answers
129 views

Make $20$ using two “$3$”s [on hold]

By using two "3"s, how can we make $20$? We are allowed to use any mathematical sign.
2
votes
1answer
28 views

Derive a formula for the number of small square base pyramids required to create a bigger pyramid?

To quote from the problem statement: "Pyramids are built using smallest pyramids of "level 1", that are used as building blocks for higher levels. Stacking pyramids of "level 1" to create ...
1
vote
0answers
32 views

Sum numbers game

$2n+1$ numbers are lined up as follows: $n$ , $n-1$ , $n-2$ , $\cdots$ , $2$ , $1$ , $2$ , $3$ , $\cdots$ , $n-1$ , $n$ At each step, one can choose any number in the line and add it to each of ...
0
votes
1answer
68 views

Can this expression be made true ? 2 _ _ _ _ = 2015

Make this expression true: 2 _ _ _ _= 2015 The underscores must be replaced by any 2 of of the operational symbols +, - , x, / (divide). And any 2 of the digits 0,1,2..9. So, you basically need 2 ...
2
votes
2answers
75 views

Probablity of $k$ balls go into at most (including) $m$ boxes, with $n$ given boxes ($m\le n\le k$)

Suppose I have $n$ boxes, and an infinity of balls. All balls are regarded the same. I randomly throw balls into the boxes, each time the ball may be thrown into one of the box, with equal ...
120
votes
20answers
8k views

Are there any open mathematical puzzles?

Are there any (mathematical) puzzles that are still unresolved? I only mean questions that are accessible to and understandable by the complete layman and which have not been solved, despite serious ...
3
votes
1answer
81 views

Is my answer correct? Expected number of coin flips to get 5 consecutive heads

I found this puzzle online. Before my question gets flagged or on hold, I know the question has already been answered here but since I tried to solve it on my own I want to check if it's correct or ...
3
votes
4answers
531 views

Math Puzzle: Largest number which cannot be written as the sum of distinct fourth powers

I've come across this question which I can't seem to solve. Write the largest number that cannot be written as the sum of distinct fourth powers. First I'm stuck with the interpretation: I was ...
0
votes
0answers
10 views

Given An initial point and final point ,How to determine the number of Co-Ordinates(x,y) such that both x and y are integral?

I have thought a lot about it and still no clue. I thought of visualising the initial point and the end point in the form of a Grid. But ,soon I was over with my resources. Problem: Given an initial ...
0
votes
0answers
27 views

Right answer probability [duplicate]

I thought I'm familiar with probability, but this question got me a little stuck: If one choose an answer to this question completely random, the probability of choosing the right one is: A) ...
1
vote
0answers
51 views

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much a day does the clock gain?

The question in the textbook is: The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much a day does the clock gain? My method: The correct ...
6
votes
1answer
70 views

A runs 7/4 times as fast as B. If A gives B a start of 84m, how far must the winning post be…?

The problem statement in the book is: $A$ runs $7/4$ times as fast as $B$. If $A$ gives $B$ a start of $84$m, how far must the winning post be so that $A$ and $B$ might reach it at the same time? ...
21
votes
5answers
4k 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 ...
20
votes
6answers
2k views

Chicken Problem from Terry Tao's blog (system of Diophantine equations)

This problem was posted by Terry Tao in his blog earlier. It's actually from his son's Math Circle. It took him $15$ minutes to solve it. I guess we all can take a crack at it. Three farmers were ...
6
votes
2answers
225 views

Which mathematical game or puzzle did you invent?

A couple of weeks ago, a friend of mine showed me a extension of a game we are all familiar with that he was working on. The game we know is called Tic-Tac-Toe, and he was working on his own version ...
1
vote
1answer
53 views

Is there a mathematical way to determine a solution for puzzle games?

Or more specifically, a mathematical way to determine HOW to solve a puzzle game. Take a look at this screenshot of a puzzle game "The Talos Principle." As you can see, the purpose of this ...
3
votes
2answers
489 views

The sum of digits of $3(3x+3)$ is always $9$ for any $x$ between $1$ and $9$

Given the following 'joke' I stumbled across today It's easy enough to figure out that the answer is always 9. Asshole. However when I tried to 'prove' this for ...
21
votes
2answers
1k views

A riddle with a witch and some gnomes (guessing numbers on hats)

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 ...
27
votes
1answer
2k views

Six Frogs - Puzzle (order reversal using special transpositions)

I had come across a puzzle: The six educated frogs in the illustration are trained to reverse their order, so that their numbers shall read 6, 5, 4, 3, 2, 1, with the blank square in its ...
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. ...
2
votes
3answers
856 views

the time at which the hour & minute hands in a clock becomes straight?

At what time exactly does the minute hand and the hour hand in a clock becomes straight between 7O'clock & 8O'clock. Iam getting the time is in between 7:05 and 7:10 but what after that. can it be ...
5
votes
3answers
6k views

Famous puzzle: Girl/Boy proportion problem (Sum of infinite series)

Puzzle In a country in which people only want boys, every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is ...
7
votes
1answer
74 views

Diagonal-free Sudoku grid

I have a Sudoku grid with the property that diagonally adjacent elements are distinct (it is also a torus under the same property). The grid offers new and exciting logical possibilites. My question ...
5
votes
2answers
127 views

A Knight and Knave Problem

There are $69$ people in a room, of which $42$ are truth-tellers (they always tell the truth) and the rest are liars (they can lie or tell the truth). You are allowed to ask any person $A$ whether ...
0
votes
2answers
358 views

How much the shopkeeper loses? [duplicate]

I struck with this tricky math question A girl went to a shop and bought a Rs.$200$ show piece. She gave a Rs.$1000$ note to shopkeeper. Shopkeeper didn't have any change so he went outside and ...
5
votes
2answers
102 views

How to solve this riddle?

How to solve this riddle? All rooms have the same shape and size. Every room has one entrance, and two exits: one on the left, and one on the right (on opposite directions). Both exits lead to a ...
0
votes
2answers
26 views

Aptitude: Time and Work

6 men can complete a piece of work in 12 days. 8 women can complete the same piece of work in 18 days, whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children ...
0
votes
1answer
31 views

Reasoning - Seating Arrangement

Eight fiends P, Q, R, S, T, V, W and Y are sitting around a square table in such a way that four of them sit at four corners of the square while the rest sit in the middle of each of the four sides. ...
3
votes
4answers
52 views

Sum of Digit Permutations

The question simply states "Let a secret three digit number be $cba$. If the sum of $cab + bac + bca + abc + acb = 2536$, what is $cba$?" I have no idea how to approach this problem. Any hints or help ...
-4
votes
1answer
76 views

How do you make the number 43 using all of these numbers:7,7,6,5 [closed]

How do you make the number 43 using all of these numbers:7,7,6,5
3
votes
1answer
91 views

Optimal strategy for 2 players Lights Out game variation

Consider a turn-based game for 2 players. They're both playing on the same board. The board is 8x8, randomly generated and each cell has 0 or 1 (with equal probabilities), for example: ...
3
votes
2answers
1k views

why 64 is equal to 65 here?

how is this possible? I know there is some trick, should someone please explain?!
0
votes
0answers
25 views

How many closed knight's tour are possible in a $8\times 8$ chessboard? [duplicate]

How many closed knight's tour are possible in a $8\times 8$ chessboard? I hae no such idea. Please give me the proof of it.
2
votes
4answers
135 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 follows: "Ms Michu has two children. We know one of the two is a girl, we call that girl Ludivine. What is ...
3
votes
1answer
61 views

on which floor does she lives?

A woman lives in a 36 floor building. There is a lift in that building. When she leaves her aprtment and goes to lift,there are 3 times chances lift will take her up than take her ...
7
votes
3answers
4k views

Father and daughter river crossing puzzle.

There are 3 men and 3 girls. lets name them ABC, A's daughter X, B's Daughter Y, C's daughter Z. Rule to cross the river: At once Only two Can go on boat. Only Men know how to drive the boat (So ...
1
vote
1answer
64 views

Finding integer solution to solve a puzzle

I have been given the following puzzle: find the smallest number that it's right most digit is 2, and if you remove that digit and place it on the left most side of the number it will double its ...
3
votes
5answers
902 views

Extending the length of a curcumference by 1 meter

I once heard the following statement: Take a piece of string and measure the length around a ball. Now add 1 meter to the string and stretch it out evenly around the ball. Obviously the ...
6
votes
6answers
6k views

A number when divided by 2, 3, 4, 5, 6 leaves a remainder of 1 but it is divided by 7 completely.

I came across a question which is as follows: Find out the smallest number which leaves remainder of 1 when divided by 2, 3, 4, 5, 6 but divided by 7 completely. What I did is given below step wise. ...
5
votes
4answers
336 views

How to formally model the “hesitation” in the hat-guessing puzzle?

Hua Luogeng (in Chinese, 华罗庚) took a hat-guessing puzzle as an illustration in a booklet focusing on mathematical induction. The following description is a literal translation from Chinese. ...
18
votes
2answers
709 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 ...