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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0
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0answers
28 views

Guess the rule of transformation of a natural number

I came across a playful problem. On a sheet of paper it is written the number $\overline{1234xy}$, where \begin{equation}\overline{1234xy}=1*10^5+2*10^4+3*10^3+4*10^2+x*10^1+y\end{equation} Five ...
12
votes
1answer
77 views

parallel resistors

Consider the set $E_b = \left\{1, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2\right\}$. This is our base set. Let's define the set $E$ as follows: $$ E = \left\{ 10^k e \mid k=0,1,2,\ldots, ...
1
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2answers
85 views

Math riddle - Forehead numbers

Three players, Annie, Billy and Katie, each have a natural number written on their foreheads. Each player can only see the foreheads of the other two. The following two things are common knowledge ...
0
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2answers
46 views

A Solution to the Classic “12 Marbles, find the one of different weight” Brainteaser

The classic problem goes like this: You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in ...
0
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2answers
90 views

All squares above 6 have an even number of multiples of 10. Why?

I was recently looking at a puzzle in Martin Gardner's book: Two brothers sell their heard of sheep, and receive the same number of dollars per sheep, as there were sheep in the heard. They ...
1
vote
2answers
19 views

Fixed points of iterates of a certain map $\Bbb N \to \Bbb N$

I have stumbled onto chains of numbers that are interesting in that, when they are split up into their digits, summed, squared, and repeating some number of times, yield the original number. This ...
5
votes
1answer
137 views

The locker puzzle - predetermined strategy

The question is related to the famous locker puzzle: The director of a prison offers 100 prisoners on death row, which are numbered from 1 to 100, a last chance. In a room there is a cupboard with ...
1
vote
4answers
41 views

Dartboard puzzle.

Given a dartboard of radius r and infinite darts.How many minimum darts you need to throw so that you can be sure that the next dart you throw is strictly less than r distance from some previous dart? ...
4
votes
1answer
59 views

A probability puzzle about mountain villages

I hope this puzzle will be of some interest. The mountain villages $A,B,C$ and $D$ lie at the vertices of a tetrahedron, and each pair of villages is joined by a road. After a snowfall the ...
1
vote
2answers
49 views

Proving that an expression returns a real non-integer number (Number 2)

Let $$a=443372888629441 = 17*31*41*43*89*97*167*331$$ $$b=(3+\sqrt{13})/2$$ $$c=(2+\sqrt{8})/2$$ $$d=(1+\sqrt{5})/2$$ How can you prove that the expression ...
3
votes
3answers
64 views

A puzzle about numbers which do not have 2 in their decimal representation

I came across this puzzle recently which I hope people might enjoy. Let $S(n)$ be the set of positive integers less than $n$ which do not have a $2$ in their decimal representation and let ...
2
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0answers
55 views

A fashion victim puzzle

Consider $n \in \mathbb{N}$ fashion-sensitive kids, each wearing a T-shirt; for simplicity, kid $i \in \{1, \ldots, n\}$ initially wears shirt $i$. Tastes over the shirts are summarized in an $n ...
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1answer
74 views

find minimum number of card which is needed to perform trick

some one ask you to choose number between $1$ and $n$ both inclusively then he shows you some card having one of more element and asks whether the card contains your chosen number or not after showing ...
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0answers
26 views

Logical Questionnaire [duplicate]

I have to go to shop but I don't have money so I borrowed \$$1000$ from friend A and \$$500$ from another friend B but on my way to shop I lost \$$1000$ and I only have \$$500$ remaining. Out of ...
2
votes
3answers
51 views

Under what circumstances are we fair in this classical dorm situation?

So I am going to college this fall. I had two roommates sharing the same room. I will bring the fridge, $\$150$, jack will bring a TV, and Kyle will bring a printer. The TV and the printer are of the ...
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0answers
32 views

Strategy for identifying traitors

I started playing the game Lost Dimension recently, and will reproduce the logic problem of the game here. Note that this would therefore have some implied spoilers from that game, although not beyond ...
0
votes
1answer
51 views

What is this problem called - 4 blocks and 3 rods?

I can't seem to recall the name of this problem however, I do remember part of its description. Basically, there are three 3 rods similar to those of an abacus and on one of the rods there are 4 ...
1
vote
1answer
29 views

Relation to find the last standing person in a circle. Possible variant of Josephus problem

Consider a set of N people standing in a circle, we kill the first person, spare the second, kill the third person and so on.. Find the last standing person in the circle. I think this might be the ...
2
votes
1answer
74 views

solve the puzzle

I have recently encountered a reasoning question that I have solved half , but I can't solve one part of it. Question : \begin{align*} 3 + 5 + 6 &= 152092\\ 7 + 6 + 5 &= 422416\\ 4 + 7 + 5 ...
-6
votes
1answer
79 views

Proving that an expression returns a real non-integer number [closed]

Let $$a = 443372888629441$$ $$b = \frac{2+\sqrt{8}}{2}$$ $$c = \frac{1+\sqrt{5}}{2}$$ How to prove that the expression $$\frac{b^a-b^{-a} - 2(c^a-c^{-a})}{a}$$ is a real non-integer number?
0
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2answers
35 views

Relation/ formula to Find the last person standing after removing people alternatively from a line?

Given N number of people, each marked as a number starting from $1$ through N, standing in a straight line where you remove folks alternatively from a line. For example in iteration 1: You would ...
0
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1answer
73 views

mathematical puzzle [closed]

If you have free time you can try to solve next mathematical puzzle. Given are four integers: 1, 3, 4, 6 and also four basic operations: multiplication ...
17
votes
6answers
6k views

Can you complete the expression $2 \underline{ }\, \underline{ }\, \underline{ } \,\underline{ } 5 = 2015$?

Can you complete the expression $2 \underline{ } \, \underline{ }\, \underline{ } \, \underline{ } 5 = 2015$ and make it correct by replacing two underscores with a selection of the ...
0
votes
3answers
60 views

Is there a pattern present?

Jack is looking at Anne, however Anne is looking at George. Jack is married, George isn't, and Anne's status is unknown. provided this info alone determine whether: a) A married person looks at a non ...
0
votes
2answers
391 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 ...
1
vote
1answer
42 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 ...
3
votes
2answers
90 views
+100

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 ...
5
votes
0answers
117 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
0answers
43 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: ...
4
votes
1answer
163 views

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 ...
6
votes
3answers
108 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 ...
2
votes
1answer
62 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 ...
1
vote
2answers
100 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 ...
4
votes
2answers
117 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
58 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
1answer
88 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 ...
3
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 ...
2
votes
2answers
80 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 ...
9
votes
2answers
214 views

Why 6 races are 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 ...
0
votes
1answer
70 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 ...
0
votes
1answer
40 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 ...
24
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
86 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 ...
3
votes
1answer
40 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 ...
21
votes
1answer
452 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 ...
-1
votes
1answer
55 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
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0answers
30 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
66 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
214 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
50 views

Find the missing dollar [duplicate]

Three friends eat at a restaurant and finally ask for the bill. They pay the 75 dollars by dividing it equally (so they spend 25 dollars per person.) The waiter takes the money to the owner, who, in ...