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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23 views

problem solving strategy excerises

given 5 bowls with the following amount of balls inside: 1 in the first, 3 in the second, 5 in the third, 7 in the fourth, and 9 in the fifth. There are two players, each player in turn is permitted ...
1
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2answers
35 views

Can't find a logical formulation to this problem

In this problem are only truth tellers and liars. When meeting two people, A and B, you ask A: "Is any of you a truth teller?", to which A replies: "If B is a liars, then i'm a liar" What are A ...
5
votes
2answers
91 views

Construct numbers using digits $123456789$ and the operations $+,-,×,÷$

From an old book I found the following question. Use the digits $1,2,3,4,5,6,7,8,9$ and the operations $"+,-,×,÷"$ with $( )$ for construct the result $100.$ During the computations the order of ...
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3answers
44 views

Turn 6 cards upside down

Six identical cards are placed on a table. Each card has number '1' marked on one side and '2' on the other. All cards are placed with '1' facing upward on a table. In one try, exactly four cards ...
0
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2answers
69 views

How can i solve this logical problem?

This problem involves two people. Person A and person B. They can either always tell the truth, or always lie. When asked, person A replies that: "At least one of us is a liar". Does person A ...
11
votes
8answers
309 views
+100

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. ...
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votes
3answers
39 views

Logic problem?? [closed]

When Paul's age in years and Evan's age in years are written down one after the other, they form a four digit number. Each of them are over 10 years old. The resulting number is a perfect square. In ...
1
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0answers
37 views

Bride Groom Problem

Let's consider a system of $n$ men and women. Each woman is paired with one man (there are only pairings between a woman and a man in this system). There are $n!$ possible distinct pairings. I refer ...
0
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0answers
40 views

Probability that two random integers do not share any digits

Draw two integers (uniformly) at random from the range $1,...,N$. What is the probability $P(N,b)$ that they have no (base $b$) digits in common? Clearly, $P(N,b)$ decreases when $b$ decreases (e.g. ...
-1
votes
3answers
41 views

How to find the total amount from given percentage

I am trying to answer this question from internet for my mathematics practice. ...
3
votes
2answers
218 views

Mathematics riddle

The question is as follows: You are taking part in a treasure hunt, where the directions to finding the treasure are given using cryptic clues. You start at a cross-roads, with roads heading out ...
2
votes
1answer
96 views

Superqueens on a chessboard.

The superqueen is a chess piece that can move like a queen, but also like a knight. What is the maximal number of superqueens on an 8X8 chessboard such that no one can capture an other? Additional ...
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1answer
44 views

How to use group theory to solve larrys square iphone app

There's a 2 d version of rubiks cube on apple app store. How can group theory give an algorithm to solve the iPhone app:larry's square.
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0answers
37 views

Using jugs filled with water problem

Given jugs $m$ and $n$ liters (WLOG $m<n$) is it always possible to get all $i$, $0 \leq i \leq n ?$ If so, prove it. If not, explain which $i$ you can get. Is there also a minimum number ...
0
votes
2answers
58 views

Who will win this game???

Two Players A & B starts to play game, they play turn by turn, A goes first. They start with two stacks of N number of coins each, Each player either have to remove one coin each from both of the ...
2
votes
1answer
63 views

Mathematics of paper fold-cutting

Take a square of paper... ... and fold it any number of times using consecutive straight folds... ... then cut off any number of pieces using consecutive straight cuts... ... and unfold the ...
1
vote
1answer
38 views

On estimating monthly credit card payment amounts (some pragmatic constraints inside)

Right off the bat, I do hope this question doesn't attract a bunch of derisive comments about my personal affairs. I give the lengthy personal anecdote because I don't have the mathematical training ...
0
votes
2answers
94 views

Evaluate $\sqrt{1 + 2\sqrt{1 + 3 \sqrt{1 + \dots}}}$ [duplicate]

I was asked to show that the answer is 3. I don't have any idea on how to proceed. Thanks!
0
votes
1answer
59 views

The number of ways people standing in a line can be holding hands

I'm writing a program to analyze the maximum unique sequences of data in a string, given certain sets of two can be interpreted in two ways. There's a bit of math that I can't figure out, I've ...
3
votes
1answer
73 views

How old was this man and his son?

A man is twice as old as his son. When his son is the same age as his father was when he was twice as old as his son, both of their ages add to 180 years old. What are the ages of the man and his ...
19
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 ...
2
votes
1answer
160 views

How to divide a $4\times 4$ square in six pieces to show that from any seven points in the square, there are two at most $\sqrt 5$ apart?

Let $R$ be a $4 \times 4$ square. For any seven points on $R$, there exists at least two of them, namely $\{A,B\}$, with $d(A,B)\le\sqrt{5}.$ (Old problem): If $R$ is a rectangular region ...
1
vote
3answers
79 views

Who robbed the bank?

Three suspects are arrested for a bank robbery. Suspect $A$ says he did not rob the bank. Suspect $B$ says he did not rob the bank. Suspect $C$ says suspect $B$ did not rob the bank. If $A$ is ...
2
votes
0answers
35 views

Minimum number of guesses on sum and product required to find two numbers.

I have a series of numbers 1 to N. A system randomly picks up two numbers and computes their sum and product. I have to guess the sum and product, The system will tell if the sum and product are ...
0
votes
1answer
44 views

Probability - Bag of Marbles Puzzle

The Puzzle: ...
1
vote
1answer
38 views

A Different Type of Knights and Knaves

You arrive on the island with knights and knaves. Like usual, knights can only tell the truth and knaves can only tell lies. You wish to determine the truth of a rumor that one of the inhabitants has ...
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votes
1answer
76 views

Find next term of the sequence [closed]

Find next term of the sequence $$4,8,61,23,46,821,652, ...$$ (Don't tell me that next term can be any number. Just find appropriate pattern, that can be described in a few words/formulas. Shorter ...
1
vote
3answers
75 views

How many are telling the truth? [closed]

Each person in a group of 5 makes a statement. Alex says ''atleast one of us is lying''. Sar says ''atleast two of us are lying''. Esther says ''atleast four of us are lying''. Gaf says ''all of us ...
1
vote
2answers
136 views

ABCDE + BCDE + CDE + DE + E = AAAAA

Today I came through this question when one of my friends asked. I don't know if this math.stackexchange community is the right place. I am new but active on other SO communities. Take me easy if this ...
3
votes
3answers
56 views

Right-Angled Isosceles Triangle covering puzzle

Consider a RAIT (right-angled isosceles triangle), from which we remove a RAIT smaller than half its area by a cut perpendicular to the hypotenuse, like this: How many RAITs are required to cover ...
18
votes
2answers
332 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 ...
0
votes
1answer
40 views

Find solutions to magic puzzle with sums

I need help to solve the folowing puzzle using linear algebra (matrix and Gauss-Jordan Method): (for example the second horinzontal line: w + w + w + z = 45 or the ...
3
votes
1answer
74 views

Understanding probabilities in a puzzle solution

I'm having a problem understanding a solution based on probabilities in the following puzzle: Puzzle: There is a "triangular" duel between the three shooters. Everyone shoots one by one, can shoot ...
8
votes
2answers
180 views

Numbering edges of a cube from 1 to 12 such that sum of edges on any face is equal

Assign one number from 1 to 12 to each edge of a cube (without repetition) such that the sum of the numbers assigned to the edges of any face of the cube is the same. I tried a bunch of equations but ...
3
votes
1answer
70 views

Can a Square be completely filled by smaller squares when none of the smaller squares have same area?

Can a Square $S$ be completely filled by smaller squares $S_i$ when area of $S_i \neq S_j$ whenever $i \neq j$? PS:The image is only meant to clarify the complete filling of squares otherwise it ...
3
votes
1answer
29 views

Most optimal way of grouping sets of game characters

I have been trying to solve this for two days now and have not come up with a good solution. Say if I have 8 character groups, like the following, how could I get them in teams of three so that all ...
2
votes
2answers
555 views

10 little dwarves

A dwarf-killing giant lines up 10 dwarfs from shortest to tallest. Each dwarf can see all the shortest dwarfs in front of him, but cannot see the dwarfs behind himself. The giant randomly puts a ...
0
votes
1answer
76 views

I'm not understanding this puzzle [closed]

At first, I was thinking, mininmum amount of sticks it takes to create the figure, and then how many draw strokes it takes to create the boxes without crossing paths...but I can't figure out what's ...
0
votes
3answers
122 views

Blue Eyes: A Logic Puzzle, has a puzzling solution (a.k.a. What does common knowledge have to do with it?)

In Blue eyes: a logic puzzle (specifically, the follow up questions), the most common answer is that it needs to be common knowledge that someone has blue eyes for all the blue-eyed people to leave. ...
-1
votes
1answer
56 views

Find the next number in the series [closed]

Can someone help me to find the next number of the following series 25,7,24,13,5,12,5,3,?
2
votes
0answers
57 views

Cookie Clicker Chocolate Egg strategy

Introduction Cookie Clicker is a silly Javascript based web game. Here is a brief description of what you do: (description taken from this question: Explain a surprisingly simple optimization result) ...
3
votes
3answers
98 views

Number of attempts needed to open lock

There are $3$ knobs for a lock $A,B,C$. Each can take $8$ positions, and for each knob there is one correct position. When $2$ of the knobs are at their correct positions, the knob opens (irrespective ...
1
vote
2answers
56 views

Area remaining after maximal number of tiles are laid on a pathway

A rectangular plot measuring $30$ m $\times$ $40$ m has a $2$ m wide pathway in the middle crosswise. Tiles of dimensions $30$ cm $\times$ $50$ cm are laid on the pathway in such a way so that no ...
0
votes
0answers
26 views

Ternary balance with unknown weight

Main references: Ternary (Wolfram MathWorld) Balanced ternary (Wikipedia) Weighing scale: Balance (Wikipedia) <quote> Balanced ternary has other applications besides computing. For example, a ...
4
votes
1answer
47 views

What exactly are the curves that are a best fit to the Harmonic Cantilever?

Let's start with a few references to get an idea: Daniel Goldwater: Harmonic Cantilever Book Stacking Problem Block-stacking problem Harmonic Series and Bricks Interesting related issues: Maximum ...
1
vote
1answer
61 views

Subtraction Game

I recently read about the Nim Subtraction Game. I have a variant, Suppose you have N stones and two players Alice and Bob, who can choose to pick either 1 stones or K stones. If Alice plays first when ...
2
votes
1answer
73 views

Russian Old Merchant Problems

Anybody know where I can find more of these old merchant problems: Lui: Please tell us a little bit about your early education. Were you already interested in math- ematics as a child? ...
1
vote
1answer
43 views

Why does the filling up of odd order magic square with numbers follow the knight movement?

Why does the filling up of odd order magic square with numbers follow the knight movement? I was reading about magic square, where I came up with the knight movement filling up of the magic square ...
4
votes
2answers
69 views

If $p(x)$ is a polynomial with integer coefficients and $p(100)=100$ what is the maximum number of integer solutions to the equation $p(k)=k^3$

If $p(x)$ has integer coefficients and $p(100)$ equals $100$ what is the maximum number of integer solutions $k$ to the equation $p(k)=k^3$. I have tried hard to solve this problem but I could not ...
3
votes
1answer
42 views

I am trying to solve a problem posited in GEB about Typographical Number Theory: how do you express “b is a power of 10”. Is my solution sound?

My solution seems too simple, and GEB has been my first introduction to TNT, so I am doubtful that I have gotten this problem correct. Of course, due to my position on the learning curve, I think the ...