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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101 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
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0answers
46 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 ...
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1answer
154 views

Probability - Bag of Marbles Puzzle

The Puzzle: ...
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1answer
43 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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3answers
83 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 ...
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2answers
533 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
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3answers
68 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
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2answers
368 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 ...
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1answer
55 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
85 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 ...
9
votes
2answers
209 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
75 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
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1answer
31 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 ...
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6answers
2k 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
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3answers
192 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. ...
2
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0answers
119 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
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3answers
115 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
60 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
42 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
51 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
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1answer
65 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 ...
3
votes
1answer
86 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
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1answer
53 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
74 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
57 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 ...
2
votes
1answer
46 views

Math riddle (ambiguous minutes/hours dials) - can you find my mistake?

I was given the following riddle: You are given a clock which has identical dials for the hours and minutes. How many times a day you can't tell the time? (i.e. the dials are indistinguishable)? I'm ...
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1answer
92 views

2048 algorithm for merging

Ok, here's a question my friend just sent me, ive mastered it to some extent, but am failing, so, please help a little: Your target is to merge these blocks in such a way that one bigger number is ...
2
votes
0answers
84 views

permutation and combination advanced

I have n sets having values less than 100. I need to find how many arrangements could be made if I pick one element from each set such that in the given arrangement there are no duplicates? NOTE: A ...
2
votes
1answer
108 views

Chessboard problem in IMO2014

This is the second problem on the IMO2014 problem list: Let n $\ge 2$ be an integer. Consider an $n \times n$ chessboard consisting of $n^2$ unit squares. A configuration of $n$ rooks on this ...
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2answers
96 views

maximum number of independent bishops on a nxn chessboard

So I came across this problem where we have to find the maximum number of independent bishops on a nxn chessboard such that no two bishops attack each other . So after drawing the cases for $3$x$3$ , ...
4
votes
0answers
112 views

How far away is that cloud?

A few weeks ago I was on an airplane and to pass the time started thinking about this problem. Using the following information, I wanted to know how far away a cloud I could see was. Under some ...
1
vote
1answer
36 views

Number of ways to travel from 1 to n in this graph?

You can move from 1 to 2, 2 to 3, and so on, step by step, till 100. Also, between the points give below, you can move directly within every pair: (10 and 60) (50 and 100) (70 and 100) (80 and ...
3
votes
1answer
74 views

Extended Calendar Cube Question

The calendar cube puzzle is famous: using two six-sided cubes, label them such that any day of any month can be represented by positioning the cubes accordingly. The solution involves allowing the ...
2
votes
3answers
79 views

The meeting of Cars

Three cars, A, B and C move towards north in a particular straight track (consider the length of the tract infinite). Another car D comes from a certain distance towards south. The car A meets B at 8 ...
3
votes
2answers
118 views

Formal approach to (countable) prisoners and hats problem.

I've found this nice puzzle about AC (I'm referring to the countable infinite case, with two colors). The puzzle has been discussed before on math.SE, but I can't find any description of what is ...
13
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. ...
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votes
2answers
39 views

Formula to have have a nonnegative integer go > 0 and < 127 [closed]

I'm working on a digital music composition where I have nonnegative integer x. I need a formula to translate x into a nonnegative integer between 0 and 127. Any ...
4
votes
11answers
547 views

Propositional logic problem about a conversation of four people who lie or tell the truth

This is obviously elementary but can't figure it out. I am taking a course named Logic and Introduction to Analysis next semester and wanted to do some reading beforehand but to figure out how deep ...
1
vote
1answer
54 views

Find the Prize With a Limited Number of Questions

This question is the final step to a much more complicated question that I have spent many hours thinking about but was never able to solve so I am hoping someone here might be able to help. The ...
0
votes
1answer
61 views

Fibonacci Numbers in Nature

Supposedly the Fibonacci sequence appears naturally in nature, and my question is how, where and I guess why? I read that one way this is so is that it models the population of honey bees under ideal ...
4
votes
0answers
98 views

Adding Numbers Pattern

A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
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 ...
1
vote
2answers
284 views

Maximum possible parts of a cake if cut n times

In how many maximum/minium parts can a round cake($\large\text{ cylinder}$) be divided with $n$ cuts when each cut is necessarily a straight line? What would be the case if we have a ...
21
votes
1answer
1k views

Is every factorial divisible by its sum of digits?

Denote by $\Sigma_d(t)$ the sum of digits in the decimal representation of the number $t$. Prove / disprove: $$\forall n\in \mathbb N:\ \ \Sigma_d (n!) | n!$$
1
vote
1answer
189 views

Lexicographical rank of a string with duplicate characters

Given a string,you can find the lexicographic rank of a string using this algorithm: Let the given string be “STRING”. In the input string, ‘S’ is the first character. There are total 6 characters ...
5
votes
3answers
621 views

Calculating probabilities in horse racing!

I've seen a few similar threads to this on different forums but they don't seem to conclude to a satisfactory answer. My question is this: If you have 3 horses, A, B, and C and you know the winning ...
2
votes
1answer
69 views

How much distance did messenger cover? [closed]

A column of troops $80$m long is moving along a straight road at a uniform pace. A messenger is sent from the head of the column, delivers a message at the rear of the column and returns. He also ...
0
votes
4answers
227 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?
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2answers
61 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
52 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 ...