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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3
votes
2answers
53 views

Can any $n \in \mathbb{N}$ be reached from 1 by doubling and summing digits?

For $n \in \mathbb{N}$, let $f(n) = 2n$ and let $g(n)$ equal the digit sum (in base ten) of $n$. Can any $n \in \mathbb{N}$ be reached from $1$ after a finite series of applications of $f$ and $g$?
1
vote
2answers
35 views

Looking for set of combinatorics problems

I'm preparing to Mathematics for Computer Science exam. What I learned from past edition of exams is fact of very often occurence of old problems. I mean more or less known problems, but possible to ...
1
vote
5answers
54 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? ...
11
votes
2answers
198 views

Smallest integer $k$ so that no Sudoku grid has exactly $k$ solutions

Inspired by this question, consider hints on a Sudoku board. A regular puzzle has a unique solution. It is clear that there are puzzles with 2 or 3 solutions, and therefore, I guess, puzzles with say ...
3
votes
2answers
1k views

Villager Logic Puzzle

Each inhabitant of a remote village always tells the truth or always lies. A villager will give only a “Yes” or a “No” response to a question a tourist asks. Suppose you are a tourist visiting this ...
2
votes
3answers
77 views

Fun logic puzzles to teach logic/proof-writing to students

Forgive me if this is too soft of a question, but I am looking for some fun, quick, and interesting logic puzzles to give to my students. I'm teaching an honors calculus course, and this will be their ...
-2
votes
1answer
30 views

How many of the three natives are bears and how many are packers? [on hold]

In a certain mythical community, Bears always lie and Packers always tell the truth. A stranger meets three natives And asks the first if he is a bear. The first native answers the question. The ...
3
votes
2answers
115 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 ...
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 ...
1
vote
0answers
35 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
79 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, ...
16
votes
4answers
11k views

How is this a number sequence 58, 26, 16, 14, 10

I recently had a IQ Test taken and we all got stuck on the same question. The question was: What comes next in the following sequence? 58, 26, 16, 14, _ The answer given in the answer sheet was 10. ...
1
vote
2answers
87 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
votes
2answers
91 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 ...
0
votes
2answers
48 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 ...
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 ...
3
votes
2answers
1k views

Logic Puzzle with Eight Clues

I am not sure where to start to solve this problem: Smith, Jones, and Rodriguez are the engineer, brakeman, and fireman on a train, not necessarily in that order. Riding on the train are three ...
1
vote
2answers
20 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
5answers
7k views

Famous puzzle: Girl/Boy proportion problem (Sum of infinite series)

Puzzle In a country in which people only want boys, every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is ...
5
votes
5answers
356 views

How to formally model the “hesitation” in the hat-guessing puzzle?

Hua Luogeng (in Chinese, 华罗庚) took a hat-guessing puzzle as an illustration in a booklet focusing on mathematical induction. The following description is a literal translation from Chinese. ...
3
votes
1answer
87 views

Puzzling Sequence [closed]

Today I was given a question that first I thought might be easy to solve but then no matter how hard I tried I couldn't solve it.(It's not really related to maths just some puzzle) if: $$ 9999=4\\ ...
8
votes
1answer
278 views

Here is a riddle that I have no idea how to solve.

Okay, so I was trying to solve this riddle found here. It is a diagram of a star with 16 points. Each point corresponds uniquely to a number between 1 and 16. The letters on each point represent a ...
5
votes
1answer
139 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 ...
5
votes
5answers
3k views

Better than random

I have been trying to solve this question, but in vain. Please help. You are given two boxes with a number inside each box. The two numbers are different but you have no idea what they are. You ...
3
votes
3answers
4k views

How to check if a 8-puzzle is solvable?

I have a 8-puzzle 1|2|3 -+-+- 4|5|6 -+-+- |8|7 How can be checked if the puzzle is solvable? Wikipedia states that it is solvable, but does not prove it. Can ...
7
votes
3answers
7k views

Finding the n-th lexicographic permutation of a string

I have an ordered set of symbols S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }. I want to find the 1,000,000-th permutation in lexicographic order of S. It is a programming puzzle, but I wanted to figure out a ...
9
votes
2answers
218 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 ...
4
votes
3answers
526 views

Probability in Minesweeper

Suppose I click a random tile during a Minesweeper game. It is a 1. During each time I click an adjacent square, what are the chances of hitting a mine? How would this change if it were a 2 or another ...
4
votes
1answer
61 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 ...
21
votes
1answer
455 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 ...
2
votes
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 ...
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
67 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 ...
0
votes
3answers
92 views

Finding four digit number ABCD such that $ABCD \div DCBA = 9$

If $(ABCD) \div (DCBA)=9$ where $A,B,C$ and $D$ are distinct and all them belong to ${0,1,2,3,4,5,6,7,8,9}$ but $A$ and $D $are not equal to zero then find $A,B ,C$ and $D$. I tried with the decimal ...
-2
votes
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 ...
-4
votes
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 ...
6
votes
2answers
4k views

How can four employees calculate the average of their salaries without knowing other's salary using RSA?

I know of a solution. But this has a limitation that information is partially passed around and there needs some trust level. I'm wondering if any variant of public-private key (e.g. RSA) algorithm ...
0
votes
1answer
97 views

Is there a general solution to the water-bucket logic problem?

Having an infinite supply of water and two containers, one for 3 liters and one for 5 liters, how would you measure 4 liters? Each step in the solution can be one of three things: Fill up a container ...
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 ...
57
votes
6answers
12k views

Logic problem: Identifying poisoned wines out of a sample, minimizing test subjects with constraints

I just got out from my Math and Logic class with my friend. During the lecture, a well-known math/logic puzzle was presented: The King has $1000$ wines, $1$ of which is poisoned. He needs to ...
0
votes
3answers
534 views

Pigeon hole principle based puzzle question

A card-board box contains 12 pairs each of three different types of hand gloves used by batsman in cricket. They are separated into single units of gloves and all mixed. you can not see the gloves ...
0
votes
1answer
52 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 ...
0
votes
0answers
33 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 ...
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
80 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?
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 ...
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 ...
2
votes
2answers
920 views

Seating Arrangement puzzle.

Not sure if its a correct place to post these kind of questions. Eight persons-P,S,Q,R,U,B,J and C are sitting in a field in a circle. Three are facing opposite side and other five are facing the ...