2
votes
6answers
76 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 ...
17
votes
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 ...
-1
votes
3answers
101 views

logical negation of a statement: any mammal that has long ears has at least [closed]

Write the negation of the following statement: Any mammal that has long ears has at least one of its predators with yellow eyes having all of its cubs that cannot fly. Write it in the logical ...
1
vote
1answer
152 views

Logic Puzzle, Two Dollar Bills

I read the following online, and I can't seem to figure it out: A bank robber is planning a heist of a high-tech bank vault. In order to exploit a weakness in the bank's security system, he needs to ...
2
votes
1answer
84 views

How to find the minimum expression(s) of a set of fixed-width bit fields?

If we define $x_1 x_2 \cdots x_n$ as a bit field of width $n$, and each element $x_i$ may be $0$, $1$, or wildcard $*$. A set of 4-width bit fields $\{0000, 0001, 0100, 0101\}$ can be aggregated ...
0
votes
1answer
56 views

Non-uniform scaling

I have 10 numbers $x_1, x_2, \dots, x_9, x_{10}$ which sum to a total of $1,000$. I want to scale these numbers so the total is equal to $10,000$, however I don't want them to scale exactly. I'm ...
2
votes
1answer
120 views

Knight Knave puzzle with three boxes

Could you please help me with the following puzzle: Consider the following puzzle: Suppose there are two box makers: Knight and Knave. Knight always writes true statements on his box, ...
1
vote
2answers
142 views

A simple riddle related to addition of odd numbers

I'm not sure if this type of question can be asked here, but if it can then here goes: Is it possible to get to 50 by adding 9 positive odd numbers? The odd numbers can be repeated, but they should ...
1
vote
1answer
114 views

Question about a puzzle in to mock a mockingbird

In to mock a mockingbird, we have the following puzzle: There are four people: A is an accurate truth teller B is an inaccurate truth teller C is an accurate liar D is an inaccurate liar Smullyan ...
9
votes
2answers
605 views

9 pirates have to divide 1000 coins…

A band of 9 pirates have just finished their latest conquest - looting, killing and sinking a ship. The loot amounts to 1000 gold coins. Arriving on a deserted island, they now have to split up the ...
1
vote
1answer
164 views

Polygon made up of 12 unit sticks with an area limit

A polygon is made up of 12 unit sticks and its area is 3 units^2. Find as many such polygons as possible. Note that a side of the polygon could be made up of more than 1 stick but a stick could not be ...
0
votes
1answer
97 views

How to calculate Team Strength for future prediction?

You are given with $4$ players name, namely Player $A$, Player $B$, Player $C$ and Player $D$. These players are grouped into two teams with two players each. A Game is played between the two team.For ...
1
vote
1answer
407 views

Gödel, Escher, Bach: $ b $ is a power of $ 10 $.

I’d like to verify if my formula correctly expresses that a number is a power of $ 10 $, using the $ \sf{TNT} $ language provided by Hofstadter in his famous book Gödel, Escher, Bach: An Eternal ...
2
votes
0answers
242 views

Three-god logic problem [closed]

Three gods A, B , and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random ...
3
votes
1answer
310 views

Correct Path To Castle Riddle [duplicate]

I'm working on the following riddle that I found to be kind of interesting, but I can't figure it out. The problem is as follows: A prince visits an island inhabited by two tribes. Members of one ...
2
votes
2answers
314 views

Sodoku Puzzles and Propositional Logic

I am currently reading about how to solve Sudoku puzzles using propositional logic. More specific, they use the compound statement $\bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p(i,j,n)$, ...
2
votes
1answer
468 views

Spivak Chapter 2, problems 27 (and 28)

To be honest, I have no idea how to even start this problem. I'm sorry I don't have any work to show, but I'm just at a blank. Help? Chapter 2: Problem 27: "University B, once boasted 17 tenured ...
0
votes
4answers
239 views

A logic puzzle from TES: Arena

Its nice when games have riddles hidden in them. While playing TES:Arena, I came across an unusual logical puzzle: There are 3 cells. If Cell 3 holds worthless brass, Cell 2 holds the gold key. If ...
3
votes
2answers
189 views

What area of mathematics is this problem asking about?

A colleague posted this on a whiteboard (as a brain-teaser I guess): A $\rightarrow$ B; B $\rightarrow$ C; AD $\rightarrow$ E; BE $\rightarrow$ C; BF $\rightarrow$ D; AC $\rightarrow$ F What is ...
-1
votes
1answer
388 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 ...
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 ...
2
votes
2answers
220 views

Four men seated in a boat puzzle

I am looking for an elegant way to solve this rather simple logic puzzle using mathematical logic (statements, conjunctions, disjunctions, implications, tautologies, predicate logic and so on). I am ...
1
vote
3answers
1k views

Solve this logical puzzle only using logical equivalencies. Is there a shorter way to do it?

Here's a puzzle: Four friends have been identified as suspects for an authorized access into a computer system. They have made statements to the investigating authorities. Alice said "Carlos ...
6
votes
1answer
345 views

To Mock A Mockingbird: Two barbers (logic puzzle)

I suspect an error in the solution given to a logic problem in the book To Mock a Mockingbird (Chapter 3 Problem 2). Problem Suppose I told you that the town contains two barbers, Arturo and ...
5
votes
3answers
1k views

Express logic puzzles with proposition calculus notation

I’m trying to solve a logic puzzle that goes like this: The police have three suspects for the murder of Mr. Cooper: Mr. Smith, Mr. Jones, and Mr. Williams. Smith, Jones, and Williams each declare ...
4
votes
4answers
3k views

What is the name of the logical puzzle, where one always lies and another always tells the truth?

So i was solving exercises in propositional logic lately and stumbled upon a puzzle, that goes like this: Each inhabitant of a remote village always tells the truth or always lies. A villager will ...
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 ...
4
votes
2answers
1k views

How to solve this type of Puzzles (Syllogism)?

I have seen lot of questions of below type predictions. I can't figure out the answer. Is there any common method to solve this ? Please consider the following example ...
8
votes
0answers
369 views

Irreversible chess [closed]

Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no ...
6
votes
2answers
359 views

Puzzle: Can arithmetic be axiomatized with a single two-term relation?

Following my question about defining multiplication in terms of divisibility, can all of arithmetic be axiomatized with a single two-term relation? Asaf Karagila comments on my question that the ...
3
votes
1answer
3k views

Logic Puzzle of the age of three sons

There is a puzzle, it goes something like this: Someone talks to a guy, and asks, Give me the age of my three sons, The other guy asks for some clues: The product of the age of the three sons (of ...
4
votes
1answer
910 views

Knights & Knaves Logic Problem Help

Can anyone please help me with this knights & knaves logic problem? It is from Raymond Smullyan's Forever Undecided. P= Proposition, and Q = Different Proposition. Properties: 1) R(P) -> B(P) ...
4
votes
6answers
2k views

Knights and knaves: Who are B and C? (task 26 from “What Is the Name of This Book?”)

I have the following issue #26 from What Is the Name of This Book? of R. Smullyan: There is a wide variety of puzzles about an island in which certain inhabitants called "knights" always ...
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 ...
9
votes
1answer
269 views

Ten people in a room

There are ten people in a room: Person 1 knows 9 people. Person 2 knows 8 people. etc. Person 9 knows 1 person. How many people does person 10 know? What is the answer and what is ...