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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Show that there exists a satisfactory assignment for the unstandard language of arithmetic $\{\textbf{0}, ', <_1\}$

Consider: $A1: \textbf{0} \not = x'$ $A2: x'=y' \rightarrow x = y$ $A3: \neg x < \textbf{0}$ $A4: x < y' \leftrightarrow (x < y \vee x = y)$ $A5: \textbf{0} < y ...
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2answers
51 views

Logic: Door to million dollars

You approach two doors. There are two men. Each man stands in front of one door. Through one door you will win one million dollars. Through the other they will take one million dollars off you. One ...
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1answer
20 views

Understanding a complex set description

I am trying to understand the following math expression, describing the possible sets of a 15 Puzzle: The expressions for tile and ...
4
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5answers
79 views

concerning a cheque

A man went into a bank to cash a check. In handling over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it and on the way ...
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2answers
45 views

Puzzle about convict who chooses length of his imprisonment

This is the puzzle I deal with for few days right now and I can't figure it out. I translated it from other language if I can improve post please comment. In the end of a trial judge sentenced a ...
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2answers
56 views

Maths brain teaser. Fifty minutes ago it was four times as many minutes past three o'clock

Fifty minutes ago it was four times as many minutes past three o'clock. How many minutes is it to six o'clock..? I have got the solution online but have doubts in it : ...
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0answers
32 views

Counting the number of cubes in an isometric view

I had seen questions in a sample aptitude test, where an isometric view of an object made up of cubes was given, with some of the cubes removed. We were supposed to count the number of cubes present ...
2
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2answers
55 views

Sudoku candidate probability

Supose a Sudoku puzzle row has four empty cells. The candidates for each cells is as follows: $3, 6, 9$ $7, 9$ $3, 6, 7$ $3, 7$ Looking at the possible cells for $3$ (cells $1$, $3$ and ...
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1answer
28 views

Independently rotating cubelets of a 2 x 2 rubiks cube?

I was reading up on 2 x 2 Rubik's cube. Wikipedia says that Any permutation of the eight corners is possible (8! positions), and seven of them can be independently rotated (37 positions). I ...
3
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6answers
176 views

What is the shortest way to write the number $1234567890$?

Here's a challenge : find the shortest way to write the number $1234567890$ . There is several ways to write the number $1234567890$ : $1.23456789 × 10^9$ $2×3^2×5×3607×3803$ $617283945×2$ But ...
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0answers
56 views

Number of paths in a grid

A common puzzle problem is to count the number of paths that start from the bottom-left-hand corner of a grid and end at the top-right hand corner, with the restriction that you can only move upwards ...
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2answers
34 views

Riddle about 3 men competing and never tying

Mr. A, B, C decided compete in athletics against each other. They competed in few disciplines. Winner got x points, second y ...
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1answer
26 views

Riddle about amusement park profit in relation to ticket's price

Price of the ticket at amusement park was cut down. In the result there was 50% more visitors in the park. At the same time profit from tickets' sale raised by 20%. What was the rebate for the ...
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11answers
1k views

A proportionality puzzle

My professor gave us this problem. In a foreign country, half of 5 is 3. Based on that same proportion, what's one-third of 10? I removed my try because it's wrong.
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2answers
52 views

Collection of numbers always in increasing or decreasing order

Anyone have any ideas on this question? I think you have to use the pigeon hole principle..but I am not sure about that? The numbers $1,2,3,\ldots,101$ are written down in a row in some order. Is ...
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2answers
38 views

Display Number as a sum so that sum of reciprocals of the summands is 1

Good Evening, Right now I am solving some Mathematic Puzzles and want to create a formula for the following: Display the Number 2008 as a sum of natural numbers so that the sum of the reciprocals of ...
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4answers
75 views

Move the last digit of $10k+9$ to the front, and obtain $70k+63$

"N" is a number and its last digit is 9. Delete the last digit (9) and write (9) to first digit, new number is 7 times "N". so whats that "N" ? Could anyone show me a way, how to solve such tasks? ...
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1answer
36 views

What is the legality of the following series?

What is the legality of the following series? 1,11,21,1211,111221,312211,132221,11133211,31231221,13111213112211,111331121113212221...
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0answers
39 views

Math Puzzle, finding a sequence with a certain property

A certain number of the $5000$ members of the Conway Mathematical Society (each of which has a different membership number between $1$ and $5000$) got together to discuss a puzzle. Much to their ...
3
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0answers
49 views

Given a number of items, how many sets of three are there where no two sets are two thirds similar?

Sorry if the title isn't proper math-talk. Hopefully I can explain it better here. So let's say we have a set. 1, 2, 3, 4, 5, 6, 7, 8, 9. I want to know how many groups of three can be made where no ...
11
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0answers
96 views

The Right Triangle Game

I am looking for a deeper understanding, particularly the optimum strategy and the maximum score as a function of grid size, of the following (single-player) game played with an $n$ by $m$ grid: ($6 ...
59
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13answers
12k views

Dividing 100% by 3 without any left

In mathematics, as far as I know, you can't divide 100% by 3 without having 0,1...% left. Imagine an apple which was cloned two times, so the other 2 are completely equal in 'quantity'. The totality ...
2
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1answer
29 views

Chord Maximisation

I am currently going back through all the "Challenge" questions in preparation for exams, and for this I do not know where or how to start, any hints would be appreciated. Now the way I have ...
6
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2answers
277 views

Find the pattern puzzle

The question is: I thought of something like: 1st box: $(7-5)*(7+5)+50=74$ Yes! 2nd box: $(21-5)*(21+5)+50 =466$ Yes! 3rd box: $(21-7)*(21+7)+50=442$ No :( That's not an option. I have tried ...
3
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0answers
88 views

Which mathematical game or puzzle did you invent?

A couple of weeks ago, a friend of mine showed me a extension of a game we are all familiar with that he was working on. The game we know is called Tic-Tac-Toe, and he was working on his own version ...
2
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2answers
74 views

Is there a solution to this Seating Plan problem?

So a colleague asked me for some Help on an interesting Problem, which we both couldn't find the optimal answer for. The event which needed it is already in the past, so this is just me trying to ...
0
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1answer
39 views

Calculate Income Of the Month [Puzzle]

Mr. Jill requires Rs 6000 per month to maintain his family. He saves 20% of any amount that he earns above Rs. 6000 but below Rs 7000 in a month. He saves 30% of amount that he earns above Rs 7000 but ...
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2answers
89 views

Math Brain Teaser! Can't solve, please help!

The sum of face values of two coins is twice the difference of the two. Find them.
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0answers
33 views

Riddle about dog running in company of soliders

Group of soliders march togheter straight in square formation 50 x 50 meters. There is the dog at the back of the formation. Dog starts to run towards the first line of soliders and then when it ...
0
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2answers
55 views

Riddle about ant going through self extendible string

Ant stands at the end of a rubber string which has 1km of length. Ant starts going to the other end at speed 1cm/s. Every second the string becomes 1km longer. For readers from countries where ...
2
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2answers
59 views

Crossword puzzle- Crossnumber puzzle

The puzzle below is a cross number puzzle, similar to a crossword puzzle except that the entries are numbers. Enter one digit per square. The thick heavy line is a separator. ACROSS: a. A prime ...
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0answers
71 views

Wedding Vows puzzle

My father came up with a puzzle and dared me to solve it. I could solve it by trial and error, but I rather want to solve it mathematically. It is the so called "Wedding Vows puzzle" where you have to ...
2
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6answers
77 views

How can I formulate the two guards puzzle to disallow references to the other guard?

An old logic puzzle goes as follows: There is a gate with two doors, each leading to a different city – Tannenbaum or Belvedere. You wish to get to Tannenbaum, but you do not know which of ...
2
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1answer
48 views

Puzzle : cable in the field

Here is an interesting puzzle taken from mathproblems.info: There is a straight cable buried under a unit square field. You must dig one or >more ditches to locate the buried cable. Where should ...
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2answers
56 views

Riddle about number of children Mr. A,B,C have

I have a riddle and I am stuck with it second day. Mr. A,B,C have in total 6 children: 5 sons and 1 daughter. John has one child more than Mr.B. Thomas has the same number of childrean as Peter and ...
7
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0answers
621 views

Is the game 2048 always solveable?

Games got me on math. I always want to play best. I don't know how to answer my question. My question is : How to show that the game 2048 is (always) solvable>? Is there any method other than ...
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1answer
46 views

x=z in minimum number of operations

I have three integers $x = 19$, $y = 7$ and $z = 27$. What will be the minimum number of operations needed to convert x to z given are the operations. $$x = x + y\\ x = x - y\\ y = x - y$$ where ...
4
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1answer
50 views

Constructing of sequences with steps already “existing” in sequence

Sequence $\{a_k\}$ is built according to next rule: $$ a_0=0;\\ a_1=1;\\ \forall n\in \mathbb{N} ~ \exists i,j ~ (0\leqslant i<j\leqslant n),\mbox{ so that } a_{n+1}-a_{n} = a_j-a_i. $$ ...
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3answers
126 views

What is the next number? [closed]

What is the next number in the following set ? $$1,11,21,1211,111221, \ldots$$
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8answers
4k views

Is Lewis Carroll's reasoning correct?

A bag contains 2 counters, as to which nothing is known except that each is either black or white. Ascertain their colours without taking them out of the bag. Carroll's solution: One is black, and ...
0
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1answer
49 views

Question on Speed and Distance

X, Y and Z move along a circular path of length 1.2 km with speeds of 6 km/h, 8 km/h and 9 km/h respectively. X and Y move in the same direction but Z moves in opposite direction. If they all start at ...
6
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5answers
2k views

Bringing the fox, the goose and the cereal across the river unharmed

Solve puzzle algebraically? I can't come up elegant and algebraical solution. There are man, fox, goose, and cereals. If the man is not beside the fox, the fox will eat the goose. If the man is ...
3
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0answers
67 views

Fisherman riddle: Combining probabilities

This is more a probabilities problem than a riddle. The riddle is: I am in a village, where a fisherman lives. The fisherman tells me that there is a 70% possibility that it will rain tomorrow. I ...
2
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1answer
80 views

Problem of the Week! [duplicate]

This week in Algebra II we are studying the Hanoi tower's. Our assignment was to find what type of formula would give the number of moves it would take to solve the puzzle. After using a T-chart ...
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3answers
95 views

solve the puzzle how many liars?

Each boy in a group of $20$ boys either always tells thuth or always tells a lie. These boys are sitting around a table. Each boy says that his neighbours are liars. Prove that at least $7$ out of ...
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1answer
60 views

What is the name of this puzzle?

Anyone knows what is the name of this puzzle:
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2answers
82 views

Winning a restricted game of Nim?

Given the following piles, find the Grundy number of the initial position and make the first move in a winning strategy given that no more than two sticks may be removed from a pile at any time. Pile ...
2
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2answers
101 views

find maximum area

Consider a problem here : There is a wall in your backyard. It is so long that you can’t see its endpoints. You want to build a fence of length L such that the area enclosed between the wall and the ...
4
votes
1answer
78 views

General approach to puzzles such as the “6 books puzzle”

Six different books (A,B,C,D,E,F) of identical size are stacked as in the figure. We know A and D are not touching. E is between two books which are both vertical or both horizontal. C touches ...
0
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1answer
69 views

Riddle: Minimum time to cross the bridge?

I've recently been asked to solve a riddle, which sounds something like that: There are 4 people on the one side of the bridge. They have only 1 flashlight. It takes respectively 1, 2, 5 and 10 ...