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Questions tagged [puzzle]

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 existing solution.

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How many lockers are open?

Q.> A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony: There are 1000 lockers and 1000 students in the school. The principal asks the ...
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0answers
20 views

How to write a good heuristic function

I have a game, that works based on the following rulesets: I have a 3x3 size board, with enemies on some of the spaces Each enemy has a type, and 3 values, to differentiate between them: health [H], ...
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2answers
21 views

3 person Knights and Knaves Problem

The problem goes as such: politicians never tell the truth and non politicians always tell the truth. A stranger meets 3 natives and asks the first of them "Are you a politician?" And he answers. The ...
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2answers
45 views

Math puzzles suitable for printing on a mug

I need to design a cup for a reception for first-year college students and i'm searching for some challenging and entertaining math puzzle or game to use. Previous years it has been used the "Three ...
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1answer
117 views

Five Similar Triangles from 4-5-6

A 4-5-6 triangle can be divided into 5 similar scalene triangles. I have the solution, but I figured out it was a 4-5-6 after putting together the component triangles. Can anyone else find it? The ...
2
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3answers
60 views

What is the minimum time needed for Shubrata and Amlan to eat 252 jackfruits?

Once Shubrata and Amlan ate 50 jackfruits in total for 3 hours and 5 hours respectively. Another time they ate 200 jackfruits for 26 hrs and 10 hrs respectively. Now what is the minimum time ...
3
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1answer
25 views

Extra information in a IID random variable?

So here's the original question: $n$ players enter a room and a red or blue hat is placed on each person’s head. The color of each hat is determined by [an independent] coin toss. No ...
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1answer
37 views

Using a straightedge, a compass, and a knife to cut a triangular cake into pieces that reassemble into a rectangle

Suppose you are using a triangular cake, a straightedge, a compass, and a knife. Using these, you are only allowed to cut triangular portions from the cake. Can you rearrange these portions (all) to ...
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1answer
33 views

Combinatorics problem on $k$ sets and partionning a set of numbers [duplicate]

consider $2k+1$ real numbers satisfying the property such that any $2k$ of them can be partitioned into two $k$ sets which exist that the sum of the numbers in each of the sets are equal. Prove that ...
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2answers
56 views

Information theory riddle about finding a gift in one of 16 boxes

There are $16$ boxes, one of which contains the gift. We have $7$ persons, who can help us by answering on any yes/no question, but one of the persons is a liar, he may not tell us the truth. We have ...
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1answer
22 views

How to find the inverse of the method to find the nth lexicographic logical permutation

I'm looking for a proper method to find the nth logical permutation of a particular sequence that is able to return the desired permutation. For example, for a sequence 1234567890, the 100,001st ...
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2answers
28 views

Problemsolving with weights and their labels

The problem is stated as follows: With a balance scale and six given weights; 1g, 2g, 3g, 4g, 5g and 6g, is it possible to make sure the labels on the weights are put on correctly only using the ...
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0answers
60 views

Solving $\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}$ [duplicate]

$$\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}$$ My approach 1st approach: Let $\sqrt{1+\sqrt{2+a}} = x$, where $a$ is a result of the lower portion of the continued nested radical and $1+\sqrt{2+a}$ is a ...
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0answers
28 views

Generating rotating groups for a seminar

One of my teachers is planning a seminar for his English class and he asked me if there was a way to generate the groups for the days other than brute-force random generating. I really think there ...
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1answer
50 views

Math optimization riddle

You have been given the task of transporting 3,000 apples 1,000 miles from Appleland to Bananaville. Your truck can carry 1,000 apples at a time. Every time you travel a mile towards Bananaville ...
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1answer
57 views

Maximum number of ufo that can visit any planet

Consider an infinite alien 2d world consisting of infinite planet, so that distance between any two planets is not same. Now at some point of time, a ufo leaves each planet and goes to planet nearest ...
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1answer
76 views

Solving the sequence $3/6, 1/2,3/4/7/6,9/14,3/4/4/5/8/7/7/6,245/256,x,x$

I need help in solving this numerical sequence. It's a pretty hard one. Commas divide each part of the sequence. The target is to find the value of the two "$x$"s and write them like a fraction/...
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1answer
72 views

Split the matrix 8-ways PUZZLE

I have a problem that has been bugging me for the last month, there is a matrix with 8x8 squares, so 64 squares, and with 8 balls placed randomly each in a square. I need to find the solution of how ...
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0answers
39 views

References about the mathematics of mazes or labyrinths

I am looking for references on mazes or labyrinths. I prefer books, but research articles are welcome, too. I am looking for the mathematical point of view of mazes, not their history or development. ...
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2answers
48 views

Help with possible algebra equation

My friend has sent me this puzzle, but I’m terrible with Algebra, could someone please explain how to solve it step by step. For example, how would I find the value of Q? Puzzle I wasn’t able to ...
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2answers
49 views

What is the total numbers of chocolates belonging to three of them?

Pial gives half of his 20 chocolates to Zunayed so that Zunayed has more chocolates, Zunayed gives half of his chocolates to Bindu so that Bindu has more chocolates than Zunayed. What is the total ...
3
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1answer
52 views

How to solve this puzzle by using Axiom of Choice? [duplicate]

In this article, at the end of page 6, it is given the following puzzle, An evil wizard has threatened a village where an infinite number of gnomes reside. The wizard will cast a spell that will ...
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0answers
264 views
+50

Infinite Rubik's Cube

Is there an infinite analog to the Rubik's Cube? What does its solution-algorithm look like? For illustration, consider the Rubik's cube with infinite tiles to a side, on all sides, with sides of ...
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5answers
512 views

Famous businessman mathematical puzzle ${}{}$ [closed]

question: A Businessman advertised two job openings for peons in his firm. Two men applied and the businessman decided to engage both of them. He offered them salary of $2000$ rupees per year. $1000$...
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2answers
116 views

What is the probability of rolling two 5s or better with 5 dice?

Preamble My question is in the context of a dice game called 31. You have 6 dice and the goal is to have the highest score. If you roll 36, you score 6 points. If you roll 35 you score 5 points and ...
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2answers
158 views

Sum of set bits in every element for a natural numbers

I was thinking of a mathematical puzzle with binary representation of numbers, but could not find a convincing answer myself. Here is the puzzle: Say for some number N, I want to find the sum of the ...
14
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4answers
402 views

Selecting a menu

While perusing old unanswered puzzle questions, I came across this one. I found it quite interesting, but a bit vague, so I've decided to recast it. A party is to be held at a restaurant. The ...
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2answers
82 views

In $x^{x^{x^{x^{…}}}}=2$, the answer is $x=\sqrt{2}$. Why not also $-\sqrt{2}$?

From this question $$x^{x^{x^{x^{...}}}}=2$$ The answer is clearly $\sqrt{2}$, but I'm curious why it's not also $-\sqrt{2}$. Am I missing something basic?
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2answers
104 views

Number of closed loops in a square grid

QUESTION: Given an $m\times n$ grid of squares, is a formula known for the number of closed loops that can be drawn along the perimeters of these squares? For a better description of what I mean, see ...
5
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1answer
206 views

Egg drop problem - minimize AVERAGE case

In the egg drop problem, you have two eggs and you want to determine from which floors in a $n$ - floor building you can drop an egg such that is doesn't break. You are to determine the minimum ...
0
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1answer
41 views

Painting Fence - Stuck to find out generalized version

Problem Statement: There is a fence with n posts, each post can be painted with one of the k colors. You have to paint all the posts such that no more than two adjacent fence posts have the same color....
7
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1answer
93 views

Puzzle group of $4\times 4$ “flip” game

I have been goofing around with the game "flip," which can be played at the following link. The puzzle consists of an $n\times n$ grid of squares that are either black or white, and when one clicks on ...
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0answers
1k views

Cover Chessboard with Domino Tiles

I have a question about a mathematical riddle which I already solved but still looking for a shorter/simpler solution: Following problem: We consider a standard $8 \times 8$ chessboard and we cover ...
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0answers
76 views

Spies - how to get an inequality?

In problem 6 from Olimpiada Matemática Española 1996 there are 16 spies. Each spy spies some of their colleagues; moreover, given any two spies A and B, if A spies B then B does not spy A. We also ...
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1answer
40 views

math puzzle: 4 digit number times 3

A four-digit number $\overline{abcd}$, and a five-digit number $\overline{efghi}$, where $a,b, c, ..., i$ are from 1-9 and are distinct. We have $\overline{abcd}*3=\overline{efghi}$. What are $a, ...
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1answer
54 views

The Ages of Mathematician´s sons

Two mathematicians meet and talk: "Do you have a son?" asked the first mathematician. "Yes I actually have three sons, and none of them are twins." answered the second mathematician. "How old are ...
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2answers
62 views

The riddles about three children

We have three children A , B , C Child A says: " I ate sweets more than B , and B ate sweets more than C " Child B says: " C ate sweets more than me , also C ate sweets more than A " Child C ...
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0answers
52 views

Maximum number of umbrellas that can be added in a one kilometer beach?

Suppose we have a beach of length $1-$km. Suppose one Day $0$, the beach is empty. One day $1$, a family comes and puts their umbrella at some point in the beach. This point is fixed forever and ...
12
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1answer
554 views

What is the order-type of the set of natural numbers, when written in alphabetical order?

We are all familiar with the standard nomenclature for the smallish natural numbers, such as one, two, three, ..., one hundred, one hundred one, ..., fifteen thousand two hundred forty-nine. I ...
11
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1answer
85 views

Partially tiling a square with parallelograms

I found the following puzzle on reddit, and am struggling to find the solution: You have an $n\times n$ square, and a supply of parallelogram tiles with side lengths $1$ and $\sqrt{2}$ and angle $...
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4answers
1k views

Upside-down equation: algebra puzzle

This quirky equation was presented to me by a fellow teacher, along with the instruction "solve it both ways up". The equation is simple enough to solve, with one integer root. What's more ...
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1answer
46 views

Puzzle on the minimum number of distinct people [closed]

There are 12 photos and there are 3 women in each of the 12 photos, left, middle and right. In each photo, the woman in the middle is the mother of the one on the right, and the woman in the middle ...
5
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3answers
195 views

Maximum Area Covered by an S-Shaped Tiling

Define an s-tile as a path of squares that makes two turns in opposite directions. For instance, if one chooses the lower left corner, the middle square of the bottom side, the center, and the ...
2
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2answers
68 views

Slant cone volume problem

I was given a a problem to solve, I thought I solved it but my answers don't look like the ones provided. The Problem A cone with radius of base r and height <...
3
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1answer
56 views

Looking for solution to “lights out” puzzle variant with multiple states

Recently in World of Warcraft, there is a puzzle that is very similar to the "lights out" puzzle where a player needs to flip switches to turn all the lights into a specific color (in this case yellow,...
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1answer
77 views

Optimizing a winning strategy for a quick tabletop game

A friend of mine recently shared the following puzzle with me: Puzzle: A circular turntable is divided into four congruent quadrants by two perpendicular lines. (Think of a circle in the $xy$-...
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4answers
54 views

Knights and knaves “I could say…”

I'm having trouble with classic knights and knaves problems that use the wording "I could say" or something similar. I haven't seen this variant discussed elsewhere, although versions of this problem ...
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0answers
31 views

Bayes' theorem for weather forecast puzzle

I found the following example of a case where Bayes' theorem could be used, on this French wikipedia page. No solution has been given though. Contradictory Forecasts According to weather station $A$,...
3
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1answer
65 views

Estimate number of cards needed to be drawn from deck before full house

Imagine we have a well-shuffled deck of cards and we keep drawing cards until there is at least one full house in the drawn cards. How many cards will we draw on average? I would be interested in both ...
4
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1answer
67 views

spaghetti hoops combinatorics variation

You may have heard about the classic spaghetti hoops combinatorics problem, which has been stated like this: "You have N pieces of rope in a bucket. You reach in and grab one end-piece, then reach in ...