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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3answers
406 views

knight and knave problem

For this question, suppose you are on the island of knights and knaves. Remember that knights always speak truth while knaves always tell a lie. (a) Suppose you come across two of the natives. You ask ...
1
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1answer
28 views

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 ...
2
votes
2answers
190 views

Nullarbor Plain puzzle

I have the following puzzle I'm trying to solve: "A man lost on the Nullarbor Plain in Australia hears a train whistle due west of him. He cannot see the train but he knows that it runs on a very ...
1
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2answers
57 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 ...
4
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2answers
53 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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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 ...
0
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2answers
302 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 ...
40
votes
2answers
7k 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 ...
4
votes
5answers
85 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 ...
3
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6answers
178 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 ...
2
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2answers
46 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 ...
1
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2answers
58 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 : ...
3
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2answers
233 views

Question about a puzzle on injecting a subset of $\mathbb{R}$ into $\mathbb{Q}$

I was just browsing through the Puzzle section on Noam Elkies website. The puzzle can be found here. The solution to the puzzle proves that any well-ordered subset of $\mathbb{R}$ is countable. In ...
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 ...
1
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0answers
33 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
votes
2answers
56 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 ...
1
vote
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 ...
1
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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 ...
2
votes
2answers
35 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 ...
1
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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 ...
2
votes
2answers
39 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 ...
17
votes
6answers
4k views

Is there no solution to the blue-eyed islander puzzle?

Text below copied from here The Blue-Eyed Islander problem is one of my favorites. You can read about it here on Terry Tao's website, along with some discussion. I'll copy the problem here as ...
3
votes
3answers
61 views

To maximise my chance of winning one prize should I put all my entries in a single draw?

Every week there's a prize draw. It's free to enter using the code from a soup tin lid. You can enter as many times as you like during the week until Monday's draw and then it starts all over. The ...
10
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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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3answers
214 views
59
votes
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 ...
1
vote
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? ...
0
votes
1answer
37 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...
11
votes
0answers
97 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 ...
3
votes
2answers
214 views

What are good methods for solving Conway's card-stacking puzzle?

Suppose there is a table with three marked spots, $A, B, $ and $C$, on which playing cards can be put, face up. Initially, an ace (1), a deuce (2), and a trey (3) are placed on one or more of these ...
1
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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
votes
0answers
50 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 ...
2
votes
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
votes
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
votes
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
votes
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
votes
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 ...
0
votes
2answers
90 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.
1
vote
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
votes
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
votes
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 ...
1
vote
3answers
351 views

Implication of three statements

Three fellows accused of stealing CDs make the following statements: (1) Ed: “Fred did it, and Ted is innocent.” (2) Fred: “If Ed is guilty, then so is Ted.” (3) Ted: “I’m innocent, but at least one ...
1
vote
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 ...
6
votes
4answers
256 views

Which sentence among the three sentences is the lie?

The second statement is the lie or the third statement is the lie. This statement is a truth, or the last statement and the second statement cannot both be truths. The first statement is the lie and ...
1
vote
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 ...
2
votes
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 ...
7
votes
15answers
29k views

A loss and gain problem

This is a very simple but confusing puzzle. A customer buys goods worth $200$ rupees from a shop. The shopkeeper selling these goods makes zero profit from this purchase. The lady gives him a $1000$ ...
7
votes
0answers
632 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 ...
4
votes
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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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 ...