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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-1
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1answer
40 views

Logic Question - Minimal Calculations Required [on hold]

Not sure were to start. Have fun.
0
votes
1answer
71 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
45 views

Find the next number in the series [on hold]

Can someone help me to find the next number of the following series 25,7,24,13,5,12,5,3,?
2
votes
0answers
28 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) ...
2
votes
3answers
85 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
3answers
52 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
19 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
41 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
48 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
59 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
39 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
61 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
36 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
31 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 ...
0
votes
1answer
79 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
69 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
81 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 ...
1
vote
2answers
42 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
90 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 ...
0
votes
0answers
23 views

A Martin Gardner problem about constructing a scoreboard given minimal information [migrated]

The following is a paraphrasing of a problem from Martin Gardner called "Tricky Track." Three schools $-$ $A,B,C$ $-$ participated in a track meet with several events. Each school was awarded some ...
3
votes
1answer
59 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
66 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 ...
2
votes
2answers
73 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 ...
11
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. ...
0
votes
2answers
35 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
9answers
382 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
49 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
56 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
86 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 ...
15
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
42 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
19 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
241 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
67 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
124 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
54 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
47 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
85 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 ...
57
votes
5answers
9k 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
98 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 ...
19
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
72 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 ...
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 ...
9
votes
1answer
98 views

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, ...
40
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 : $$3\times 4=8$$ $$4\times 5=50$$ $$5\times 6=30$$ $$6\times 7=49$$ ...
2
votes
2answers
324 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
84 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?