Questions tagged [puzzle]

For questions about the mathematical principles behind puzzle, games, riddles, or their possible solutions. Questions that are not strictly mathematical in nature should be asked on Puzzling Stack Exchange.

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51 views

Let there be 16 people in a room each with distinct piece of information. Whenever two person interact, they share all the information that they have gained till that time. For instance if person $A$ ...
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How many balls can fit in a house shaped box?

Consider the following house shaped box with the indicated measures: I need to get the best possible approximation of how many balls of 3 inches of diameter can fit in this box without exceeding the ...
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Optimal Solution to a Game With Two Sequences of Bits [duplicate]

I was given a nice riddle, and solved it, and I can't tell if my solution is optimal or not. The riddle is a follows: Two infinite sequences $a_n, b_n$ of bits are randomized. The sequence $a_n$ is ...
351 views

In a competitive sort of exam, the following question was aimed at 8th graders and above- Sophie had written the numbers 1 to 22 in the 22 discs in the figure, but Adelaide, her big annoying sister, ...
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Is there a general way to find the amount of a given shape in an composite shape like this one? [closed]

I came across one of these puzzles you find across the internet and am interested in gaining a deeper understanding. I have counted the number of traingles by labelling the vertices alphabetically ...
63 views

Can anyone solve the "PLANTERSPEANUTS Puzzle"?

PLANTERSPEANUTS Puzzle: In the early 1950's the makers of Planters Peanuts sponsored a contest and offered a prize to anyone who could determine the number of ways to spell PLANTERSPEANUTS by moving ...
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Knights, Knaves and Normals Puzzle

Problem Statement You are on an island inhabited by three types of people: knights (always make true statements), knaves (always make false statements) and normals (sometimes make true statements and ...
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Truth-tellers, liars and ambiguous, solution verification

Consider the following problem In a certain country, there are three kinds of people: workers (who always tell the truth), businessmen (who always lie), and students (who tell the truth and sometimes ...
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Puzzle: binary number shrinkage on operation

Given a random binary number with n digits. Define operation P: count number of ones, suppose there are k ones in this binary number, then flip k-th digit(1 to 0, 0 to 1) counting from left(or right, ...
111 views

Puzzle: Good card of 2021*2021 cards of 2021 colors

Assume there are 2021 kinds of colors, and for each color, we dye 2021 cards with this color. Now we put these 2021*2021 cards in a straight line. We define a card as "good" card, if the ...
67 views

Minimum Number of Clues for Unsolvable Sudoku

I am going to make a distinction between "unsolvable" and "invalid" Sudoku. A Sudoku is unsolvable if there is no way to fill in all the spaces without violating one of the rules ...
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Minimum cost incurred for covering the floor with tiles

Alex plans to cover a rectangular floor of dimensions 9.5 meters and 11.5 meters using tiles. Two types of square shaped tiles are available in the market. A tile with side 1 meter costs 100 dollars ...
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Car, gas, crow problem - looking for analytic solution

I made up this problem recently. possible configuration Imagine you are lost in a car on a long circular road in a hot desert. You have enough gas to go halfway around the circle. There is a gas ...
51 views

Time Consumption by a super computer to solve a puzzle

I have a 4x3 cubic picture puzzle with 6 correct answers. Each piece in an inch^3 (l=b=h=inch=2.5cm). I can figure out the arrangements of this puzzle i.e. Each block in the puzzle can move in 24 ways ...
95 views

who is the knight, knave and spy?

A, B and C are one knight (always tells truth), one knave (always lies) and one spy (can lie or tell the truth). A says "B is a spy" C says "A is a knave" B says "you have ...
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Is it possible to solve the Rainbow Hats Puzzle using polynomial equations?

I've stumbled upon the Rainbow Hats Puzzle which has the following conditions: Seven prisoners are given the chance to be set free tomorrow. An executioner will put a hat on each prisoner's head. ...
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How to create a cube out of uneven sides [closed]

We are given: four pieces of wood; each piece is 10 cm long, 10 cm wide, and 2 cm thick two pieces of wood; each piece is 12 cm long, 12 cm wide, and 2 cm thick An 8 oz bottle of wood glue Provide ...
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Puzzle of renting rooms?

I have a doubt in this question :- How many students turned up for renting the rooms? , for convenience I have posted the same question below also Sara has a house which she wants to convert to a ...
87 views

Average number of days to reach hell?

I came across a puzzle over the internet(https://www.interviewbit.com/problems/gates-of-heaven/). Amanda dies and reaches at the gate of heaven. She has three doors in front of her out of which only ...
102 views

Light bulbs in a high dimensional grid

Consider a $n \times n \times n$ array of light bulbs. In each step, one can flip lights from on to off and off to on along a 1d row in the $x$-, $y$- or $z$-axis. Suppose one has a configuration that ...
30 views

A Leapfrog in the Array

Initially array contains $n$ numbers(integers) from $1$ to $n$ and the number $i$ is located in the cell with the index $2i - 1$ (Indices are numbered starting from one) and other cells of the array ...
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Dense landmines on a unit square - One unoriginal and one original problem (I think)

Earlier today I shared problem 1 with my friends and after solving it with relative ease, one of them asked if a modified version of the problem had a similar solution. For the next hour we worked ...
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If "AQUARIUMS" is coded as "CCKOSTUWW", then what is the code for "BARBIEQUE"?

The following question was asked in an online assessment by Goldman Sachs, for Engineering undergrads. If "AQUARIUMS" is coded as "CCKOSTUWW", then what is the code for "...
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A $5\times 5$ square with $+1$ and $-1$

This is a problem from the Monthly Contest of the Berkeley Math Circle in 2001/2002. The Problem A 5 ×5 square has been dissected into a unit square grid. One of the unit squares has been filled with ...
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Is there a general solution for an equation such as N - M = 2021 where N is four digits and M is three digits of N

The question is, given N of four digts and M which is based on any three digits of N (but in the same order as those of N) and the difference between N and M is 2021, what is the original number N? ...
64 views

How many unique combinations are possible if category contents are limited?

I'm working on a personal project and came across an algorithm problem which stumped me. I need to know whether a user has given my program the correct parameters to create the amount of random ...
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Edgematching tiles

Consider a 3×3 grid. Now, look at the patterns which generate 1 to 7 dots around the edges, taking into account rotations and reflections. Turns out there are 49 patterns, as seen in the set below ...
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Know the probability of $A$ beating $B$, also $B$ beating $C$, what's the probability of $A$ beating $C$ three games in a row?

Here's a question from my probability textbook: When a chess game is played, the better player has a ${3\over4}$ probability of winning and the worse player has a ${1\over4}$ probability of winning. (...
446 views

Scores achievable in a game of darts

This is from an italian math competition. In the game of darts below a player is able to reach points only of 105, 30, 14 (either exact center or on the border). The final score is the sum or all ...
367 views

A way to express 100 by using the first four natural numbers [closed]

Is there a way to express 100 by using the first four natural numbers in order? The numbers 1, 2, 3, 4 can be linked by using $+$, $-$, $\times$, $\div$, $($ $)$, $!$ and exponents are also allowed. ...
51 views

How to Find Total People By Their Total Weight?

imagine you are on a room where 4people lived. let's consider there weight are below: P1 = 82kg P2 = 62kg P3 = 49kg P4 = 73kg after sum we can see their total weight are 266kg (P1+P2+P3+P4 = 266kg) ...
166 views

Is it possible to guess a number from an infinite range with yes or no questions?

(I hope this qualifies as a math question; it might just be a puzzle.) I've had a thought experiment a few days ago: Assume you have a machine that randomly picks a whole number from 1 to infinity, ...
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Find total number of bikes in the town

In a town, there are 33 families that own either 1, 2, or 3 bikes. The number of families that own 1 bike is equal to the number of families that own 3 bikes. What is the number of the bikes in the ...
44 views

Intuition to move-optimality in Sokoban

The puzzle game of Sokoban has been fascinating to me since I was a child. It is played on a rectangular grid. Each square may be empty ( ) or contain a wall (...
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Tic Tac Toe on an infinite grid

Imagine playing tic tac toe, but rather than the standard 3 by 3 grid, the board extends indefinitely in every direction. When playing the usual game, one player must get three squares in a row to ...
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Why pawns starting at chessboard squares $(1,1)$ and $(8,8)$ that move orthogonally at each step will never swap positions?

Let's say we have a chessboard (i.e an $8×8$ grid). Let's assume each cell is identified by two coordinates (integer numbers) ranging from $1$ to $8$. Assume to have a red pawn in position $(1, 1)$ ...
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The Strategy of Battleship

Battleship is a children's two-player game where each player places different sized "ships" on a grid (usually 10*10) of squares. Players then take turns "firing" at one square on ...
109 views

How to solve the Tower of Hanoi with L pegs, a maximal height H, and the goal is to discover the largest disc.

I've stumbled upon an interesting variation of the Tower of Hanoi problem. Here are the conditions : You have $P$ pegs ; On each peg can stack a maximum of $H$ discs ; Discs can be of various size, ...
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"No students are athletes" but "some teachers are both athletes and students"

I was reading some logical test here. I reported it down below Given the following premises, state whether the conclusions are true, false, or unknown: All athletes are coaches, but not all coaches ...
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Minimize final marks of the student as per the marking scheme provided in the question

Question:- The scores given by three of the four professors are 45, 49, 52 for each of 2 students Alex and Dan. What is the minimum possible final score of any student ? My approach:- Assuming the ...
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Math for sequential movement puzzles? [closed]

It feels like there should be some area of math that can be used to make sequential movement puzzles like the 15-puzzle or Sokoban puzzles easier to solve. I guess for symmetrical examples like the 15-...
101 views

Sum in Magic star puzzle

I have the following problem: Place the first 11 natural numbers in the circles so that the sum of the four numbers at the tops of each of the five sectors-beams of the star equals 25. I came up with ...
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Maximum value of products the person can buy

D-bay, an online clothes and fashion store, is giving a 20% cashback on purchases worth €1000 or above made on its website. (i.e. when you purchase something worth, say, €3000, your account will be ...
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Puzzle ranking numbers

There are 10 distinct numbers in a list. Except the 1st and 10th numbers, the value of each number lies between the value of its immediate neighbors. If the 4th number is less than 7th, what is the ...
220 views

Range $[n,2n]$ containing smallest positive integer $x$ such that $x^x$ contains digits $2016$ in a row

How do I find a range $[n, 2n]$ such that it contains the smallest positive integer $x$ such that $x^x$ contains the digits $2016$ in a row (consecutively), up to sufficiently high probability? I ...
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Generalisation of this circular arrangement of numbers from $1$ to $32$ with two adjacent numbers being perfect squares

I got this interesting arrangement of numbers from $1$ to $32$ in a group in Facebook- This being an interesting property to look at, I was trying to figure out whether $32$ is something special, or ...
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Expected number of cards drawn to get two consecutive aces

Here is a question from my probability textbook: A person draws cards one by one from a pack and replaces them till he has drawn two consecutive aces. How many cards may he expect to draw? I'm not ...
Proving I cannot fit a parallelepiped inside another one if it has larger dimensions using the width $\sup\limits_{x,y\in A}\langle s, x-y\rangle$
Assume that I have a parallelepiped $A$ that has the following dimensions: $w_{A}, l_{A}, h_{A}$ s.t. $w_{A}+l_{A}+h_{A}= 115$. Consider another parallelepiped $B$ with dimensions $w_{B}, l_{B}, h_{B}$...