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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1answer
147 views

Balancing the weights of the vertices of a graph by averaging along the edges.

Suppose that you have a graph, and someone assigned real numbers to every vertex. You can modify these numbers by replacing the numbers on two adjacent vertices by their average. Your goal is to reach ...
3
votes
2answers
1k views

Flipping Cards Probability

You have a deck of cards, 26 red, 26 black. These are turned over, and at any point you may stop and exclaim "The next card is red.". If the next card is red you win £10. What's the ...
2
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0answers
245 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 ...
1
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1answer
37k views

What three odd integers have a sum of 30? [duplicate]

I've been asked the following question: What three odd integers from the set {1,3,5,7,9,11,13,15} that when summed together equals to 30? Note that any integer can be used more than once. Is there ...
3
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2answers
5k views

Jigsaw Puzzle Help

I have a puzzle I'm trying to solve and I have all the border pieces set out but I'm pretty sure some are missing. How do I figure out how many pieces are in the border? It's a 1000 piece puzzle and ...
3
votes
3answers
4k views

How many distinct ways to climb stairs in 1 or 2 steps at a time?

I came across an interesting puzzle: You are climbing a stair case. It takes $n$ steps to reach to the top. Each time you can either climb $1$ or $2$ steps. In how many distinct ways can you ...
1
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2answers
370 views

puzzle 3-d visualization

729 small cube are painted pink on each face and then arranged to form 27 identical middle-size cubes.Each middle size cube is painted black and then arranged together to form one large cube. And ...
2
votes
4answers
193 views

Probability interview question

Suppose we have three positive integers $A, B, C$. We randomly choose an integer $a$ in the range $[0,A]$ and an integer $b$ in the range $[0,B]$. Find the probability that $a + b\leq C$. I am unable ...
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1answer
35 views

Some kind of encrypted message in a computer game [on hold]

I'm not sure whether this is a place where I can ask this, but if anyone can help me please do so. I play an MMORPG game where many races have different histories in their books that players can ...
4
votes
0answers
77 views
+50

Cover the grid graph with simple cycles

I have a two dimensional n x m grid graph. And I want to find in how many ways this grid can be covered with simple cycles (it can be a one cycle or it can be many ...
4
votes
1answer
211 views

What function does this infinite series represent?

$$\frac14+\frac{x-4}{2!x^2}-\frac{(x-4)(2x-4)(3x-4)}{4!x^4}+\frac{(x-4)(2x-4)(3x-4)(4x-4)(5x-4)}{6!x^6}\mp\ldots$$ Can anyone deduce the sum of this series?
7
votes
1answer
95 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 ...
3
votes
1answer
45 views

find a group of lowest N numbers so that no 2 pairs have the same bitwise or

I am trying to find the lowest group of N numbers (i.e. N=1000) so that no 2 pairs from the group have the same bit-wise or. more specific need to find a group $A = \{a_1,a_2,a_3,..,a_N\} $ such ...
1
vote
1answer
1k views

what is maximum number of points of intersection between the diagonals of a convex octgon?

What is the maximum number of points of intersection between the diagonals of a convex octagon (8-vertex planar polygon)? Note that a polygon is said to be convex if the line segment joining any two ...
2
votes
3answers
519 views

Probability of an expected outcome

I'm in a class titled "Puzzle Based Learning" and we were given this problem: There is a new game show and you are the participant. There are two doors, each has a suitcase with gold coins ...
1
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0answers
35 views

A harder long division puzzle than the first; what should “Algebra I” solution look like?

Here's another problem, significantly harder than the first, but still accessible to target audience. The statement of the problem (i.e., northwest corner only) comes from a PennyDell puzzle magazine: ...
6
votes
3answers
87 views

“Long-division puzzles” can help middle-grade-level students become actual problem solvers, but what should solution look like?

This is my first post. I hope it's acceptable. EDIT Since there are people to whom such notation is foreign, I will point out that the problem represents KRRAEE / KMS, where PEI is the quotient and ...
1
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1answer
36 views

Can I find the frog jumping on leaves? 2 “contradictory” answers

I've encountered this question and found two "contradictory" answers to it. of course they are not really contradictory, but I'm having some trouble explaining why not. Say there is a frog standing ...
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votes
0answers
40 views

Puzzle, can anyone help solving this? [closed]

Could anyone solve this? been thinking about it all day and starting to feel stupid. Q12 and Q16 on http://www.arealme.com/iq-2015/en/
5
votes
0answers
95 views

Puzzle - In how many pairings can 25 married couples dance when exactly 7 men dance with their own wives?

Each married couple as well as each dancing pair consists of a man and a woman. How many possible pairings are there? Here is the same question with a different amount of couples. I read the answers ...
1
vote
2answers
87 views

Three knights on a 3x3 chess board

There are two white knights (W) and black nights(B) positioned at a 3x3 chess board. Find them minimum number of moves required to replace the black knights with the whites.Any type of move is ...
1
vote
4answers
328 views

How many faces does the resulting polyhedron have?

Take a regular tetrahedron of edge one. Also take a square-based pyramid, whose edges are all one (therefore the side faces are equilateral triangles of same size as the faces of the tetrahedron). ...
2
votes
1answer
56 views

P. Winkler's puzzle “Inscribing a Lake in a Square”

This is a puzzle from P. Winkler: "Show that, given any closed curve in the plane, there is a square containing the curve, all four sides of which touch the curve." I was NOT able to solve it quickly ...
2
votes
1answer
84 views

Is there an equation that can lead to the correct pattern for the answer to this riddle?

Here's a riddle I came across recently: There’s a group of six friends who are all musicians. One day, they decide to have a few performances between themselves so that they can hear each ...
4
votes
2answers
111 views

Maths Puzzle: Partitioning a set into two disjoint sets

Le $X$ be the set of all non-empty subsets of $\{a,b,c,d,e,f\}$. So $X=\{a,b,c,d,e,f,ab,ac,ad,ae,af,bc,bd,be,bf,cd,ce,cf,de,df,ef,abc,\cdots,abcdef\}$; i.e., $|X|=63$. We want to partition $X$ into ...
2
votes
1answer
56 views

The Sieve of Alice- Number theory Riddle

I am trying to prove the result for a problem which I am unable to do so! The answer is simply $\frac{N}{2}$ when N is even and $\frac{N}{2}+1$ when $N$ is odd. But I do not see why?? Can you give me ...
2
votes
6answers
1k views

A coin-weighing puzzle with 80 coins

In 80 coins one coin is counterfeit. What is minimum number of  weighings to find out counterfeit coin? PS: The counterfeit coin can be heavy or lighter.
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votes
3answers
1k views

Place maximum Rooks on a chessboard

I am given a chessboard of size $8*8$. In this chessboard there are two holes at positions $(X1,Y1)$ and $(X2,Y2)$. Now I need to find the maximum number of rooks that can be placed on this chessboard ...
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votes
1answer
245 views

Nice combinatorics puzzle [closed]

INTRODUCTION Around 1980 my father told my a simple yet interesting mathematics puzzle. It was similar to the "two professors puzzle". I don't remember all the details, but it had three "I don't ...
2
votes
2answers
72 views

Simple Puzzle: A Matter Of Time

I am trying to solve a simple puzzle: Fifty Minutes ago if it was four times as many minutes past three O'clock, how many minutes is it to six O'clock. I tried solving it: Let x be the minutes past ...
0
votes
1answer
69 views

How should one go about deciphering “ZPLKKWL MFUPP UFL XA EUXMFLP”? [closed]

The Princeton companion to mathematics says, "it is just possible to work out the meaning of the above example by matching letter patterns to those commonly seen in English, but it is quite ...
3
votes
2answers
200 views

Checking Sudoku - sufficient sums

Are the following condition sufficient for checking if solution of Sudoku with (extended output) is valide : sum of values in each row, column and subsquare is equal to 45 and sum of squares of ...
0
votes
2answers
106 views

Liar - Truth-Sayer - Tourist Problem. Construct the answer with the given 2 sub-statements.

A tourist A comes to a country where people are divided into two categories: Liars (L) and Truth Sayers (T). Ls always lie and Ts always speak the truth. Intending to walk to the capital, the tourist ...
2
votes
0answers
44 views

Why 6 races is not sufficient in the 25 horses, 5 tracks problem

The horse-racing puzzle has been asked on mathSE several times (1, 2, 3, 4); there is also a generalization. I restate the puzzle below: 25 horses all run at different speeds. You can race 5 ...
2
votes
1answer
133 views

Number of horse races to determine the top three out of 25 horses [duplicate]

This is a short mathematical puzzle from mindciphers.com which says : The London racetrack needs to submit its top three horses to the Kentucky Derby next month in order to compete for a prize. ...
12
votes
2answers
371 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 ...
6
votes
3answers
154 views

How to express “b is a power of 10” – Typographical Number Theory in Gödel Escher Bach

The book Gödel, Escher, Bach (GEB) by Douglas R. Hofstadter introduces a formal system called “Typographical Number Theory” (TNT). It's essentially first order predicate logic over the universe of ...
0
votes
1answer
37 views

Maximum number of teams of three people such that each team is built in one of two ways

A coach picks team members in two ways:   A. The team of three people should consist of one experienced participant and two newbies. Thus, each experienced participant can share the ...
22
votes
3answers
5k views

Why does this age calculation trick work?

The trick works like this: Take the current date in the format yyyymmdd and subtract it with your date of birth taken in the same format. Drop the last four digits to get your age. For example, I was ...
0
votes
1answer
81 views

A puzzle about choosing one of 9 doors with signs on them

This problem involves logic-based math, I tried making truth tables for this problem but I don't think you can because there are 9 doors! Below is what I came up with but I want to know if there is a ...
10
votes
0answers
198 views

Finding real money on an even stranger weighing device

You have $n$ coins which each weigh either $20$ grams or $10$ grams. Each is labelled from $0$ to $n-1$ so you can tell the coins apart. You have one weighing device as well. At the first turn you ...
4
votes
1answer
1k views

Can you make an equilateral triangle from 3identical trapezoids?

Is it possible to make an equilateral triangle from 3 identical trapezoids? If so, what angles would be needed in the trapezoids?
5
votes
3answers
2k 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 ...
4
votes
2answers
658 views

Maximizing an algebraic expression using brackets

It's a riddle of sorts: given a list of numbers $\alpha_1 \dots \alpha_n$ and operators $o_1 \dots o_{n-1}$ which can be only $\times\, \mbox{or}\, + $ if the above is a specific algebraic expression ...
2
votes
5answers
653 views

balance scale problem for 13 (not 12) items

The 12-item balance scale puzzle is very familiar. The object is to find the lone non-standard item (if one exists) out of a group of 12 seemingly identical items, using a balance scale and a maximum ...
3
votes
1answer
36 views

Diophantus' Lifespan

Today I saw Diophantus' Epitaph. For those of you who don't know it and don't feel like googling: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone tells how old: 'God ...
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votes
1answer
51 views

Krypto analysis

The game Krypto is where you get 5 numbered cards dealt with you by the dealer and then a sixth card that you must connect the five cards to with mathematical symbols. The values of the first 5 cards ...
2
votes
0answers
20 views

Symbolically formulate the two guard problem so it can be solved by a computer

Take the classic two guard riddle (I don't know where the origin of this riddle is, so I'll take the version from http://www.calpoly.edu/~mcarlton/riddles.html): You stand at a fork in the road. ...
3
votes
1answer
64 views

Frazzle game question

In $7^{th}$ grade, in order to learn divisibility, memory, and focus, my math teacher had my pre-algebra class play a game called Frazzle. To play the game Frazzle, each person went around the room ...
1
vote
1answer
49 views

3D Extension of a Fun Geometric Series Puzzle

After being inspired by this question, and in particular Semiclassical's excellent response and generalisation, I thought of another generalisation to a 3-dimensional plane.: Suppose you start at ...