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.
3,228
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Identify $d$ heavy coins where $d$ is unknown.
You are given $N$ coins which look identical (assume $N = 2^k$). But actually some of them are pure gold coins (hence are heavy) and the rest are aluminum coins with thin gold plating (light). You are ...
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34
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How many locks and keys: combinatorics problem [duplicate]
A village keep all their most precious belongings in a vault. The vault has a certain number of locks, each lock with an individual and specific key. The people in the village want to make sure that ...
1
vote
1
answer
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Expectation of removing subtree
You are given a rooted tree with n nodes. On each step, you randomly choose a node and remove the subtree rooted by that node and the node itself; until all of them have been removed (that is, the ...
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75
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The best strategy that the fireman should use in this problem is?
Problem:Suppose there is a building with $10$ floors. Each floor has only one room and each room has exactly one person in it. On the first floor there is a child in the room who weighs $10$kg, on the ...
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1
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93
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Can we generate a valid $9\times 9$ sudoku using this algorithm?
Begin with a board of $9*9$ cells, each of the cells has no value but is possible to contain a number from $1$ to $9$ (I will call the numbers can be assigned to a cell is guesses; the amount of ...
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1
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1
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Expectation problem of postman
A postman brought N letters to a house with two letter-boxes. Since the two boxes were empty, he puts 1 mail in each of the two mail boxes. Then he chooses one of boxes with probability proportional ...
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80
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Can anybody tell me how to find the value of $\alpha$?
I don't know how to find the value of $\alpha$:
$$(\sqrt{3}+\sqrt{2})^\alpha + (\sqrt{3}+\sqrt{2})^\alpha = 10$$
I tried to simplify it to
$$(\sqrt{3}+\sqrt{2})^\alpha=5$$
then take the ($\ln$) of ...
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Limit of the ratio of series
Prove or disprove the existence of a function $f : \mathbb{N} \rightarrow \mathbb{N}$ such that the following three properties are satisfied
$f(n) \leq n$ for each n;
The limit $\lim_{n\rightarrow \...
3
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2
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168
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+50
Counterfeit money, guaranteeing a profit
Bob and I found two 50 dollar bills out of nowhere. We know they're either both legitimate or both counterfeit. If they're legitimate, they're worth 50 dollars each, otherwise 0. I get one 50 dollar ...
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Sequence Limit and Series Ratio [closed]
Does there exist a function $f : \mathbb{N} \rightarrow \mathbb{N}$ such that the following properties are satisfied?
$f(n) \leq n$ ;
$\lim_{n\rightarrow \infty}\frac{f(n)}{n} = 0$;
$\lim_{m \...
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80
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Expected number of children until more girls than boys
Consider a couple that has decided to have children. They will continue having children until they have more girls than boys. What is the expected number of children they will have?
- 254
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68
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Puzzle of an ant rearranging stacks of seeds in a line [duplicate]
Interesting puzzle that I haven't been able to solve or find a solution to.
An ant rearranges a line of stacks of seeds as follows:
With each iteration, the ant goes to each stack in order and grabs ...
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1
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1
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Infected Dinner Brainteaser
I came across this brainteaser online that I found quite confusing:
There are $1000$ people having dinner at a grand hall. One of them is known to be sick, while the other $999$ are healthy. Each ...
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1
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A Simpsons Riddle [closed]
This riddle (from Amann and Escher) has been bothering me more than it should. What is going on here? I'm not sure I see how to translate this into the sort of propositional logic I can manipulate via ...
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Check my solution on a card flipping game
I'm trying to solve puzzle. Can someone please check my solution? Thank you!
I have four cards with values $1,2,3,4$ faced down. Each turn, I can either flip a card or do nothing. If I flip a card, I ...
- 1,335
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1
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Defective clock questions - Watch gaining 3 minutes every hour
An analog watch gains 3 minutes every hour. If it is set right at 11 a.m. on February 21st, 2012 when will the hour hand of this defective watch and a correct watch be at the same position ?
My ...
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22
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1
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Impossible? Finding a closed loop on a six-sided die that crosses face $n$ exactly $n$ times, without returning to a face from one step before
I'm new here, so please tell me if I'm doing anything wrong.
Here is a puzzle that I came up with, which I believe falls someone in the realm of graph theory or topology (I could be very wrong, please ...
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1
answer
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Peter winkler's "Numbers" puzzle "Zeroes, Ones, and Twos"
I have a problem with the solution for the (b) part of the problem. The problem is as follows:
Let $n$ be a natural number. Prove that $2^n$ has a multiple whose representation contains only ones and ...
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1
answer
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Family Members Birthday Dates all different, but our birthdays will fall on same day, even Leap Years. There is a total of 9 in this Birthday Club. .
I can compile a list if needed and post, but I noticed this over 50 years ago, My Father, My Brother and Myself our Birthdays fall on the same day of the week every year. Even Leap years, that does ...
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1
answer
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Using tricks to Maximize a Product of Binomial Coefficients $\binom{n}{x} \times \binom{n}{b - ax}$
I'm trying to find a solution to the following problem without resorting to brute force:
\begin{equation}
\text{maximize } \binom{n}{x} \times \binom{n}{y}
\end{equation}
subject to the constraints:
\...
- 1,085
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1
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99
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Double the marbles in bucket to produce empty bucket [closed]
Three buckets have marbles. You are allowed to double the number of marbles in a bucket by borrowing from one of the other two buckets. Prove that it is possible to produce an empty bucket with a ...
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Barge Problem from 26 Years of Posing Problems [closed]
I'm struggling to find the solution this problem:
A boy at the stern of a canal barge leaps off onto the tow path and while the barge keeps moving, runs along the path until he gets to the bow, where ...
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1
answer
62
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Dropping eggs from a building with unknown floors
With two eggs and a building with 100 floors, what is the optimal strategy for finding the lowest floor at which an egg will break when dropped? Followup: What if the number of floors of the building ...
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0
answers
31
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Polynomial guessing with 2 queries [duplicate]
Alice is allowed to choose an arbitrary polynomial p(x) of any degree with nonnegative integer coefficients. Bob can infer the coefficients of p(x) by only two evaluations as follows. He chooses a ...
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Circular ring of 19 cells. Find minimum number of targets to make all inactive.
Imagine a circular ring of 19 cells. Each cell has a coronavirus inside it: either active or inactive. Scientists have developed a special drug that can target a specific cell (of your choice). When ...
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0
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49
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Guess if it's bigger or smaller number [duplicate]
Alice writes two distinct real numbers between 0 and 1 on two chits of paper and places them in two different envelopes. Bob selects one of the 2 envelopes randomly to inspect it. He then has to ...
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A regular hexagon is tiled with diamonds in three orientations. Prove that the same number of tiles appear in each orientation. [duplicate]
A large regular hexagon is cut out of a triangular grid and tiled with diamonds (pairs of triangles glued together along an edge). Diamonds come in three varieties, depending on orientation; prove ...
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35
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Ants on a 5-foot pole with a middle ant
Alice starts in the middle of a 5 foot pole. There are n other ants
placed randomly on the pole and they start scampering in random directions with constant speed of 1 inch per second.
Alice has a ...
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How to solve a prime number-logic problem
I am sitting with two other people who are wearing hats with the prime numbers 5 and 11. My hat has a prime number also, but I don't know what it is, nor do each of them know their numbers. It is also ...
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2 dice -> 9 cards
Alice has two standard dice with labels 1 thru 6. When she rolls them and adds their labels, she gets a distribution over integers in [2, 12]. Bob has nine cards, each labeled with some real number. ...
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Maximum tiling by Y Hexomino
"Y Hexomino" has a shape as shown in the picture.
What is the maximum number of Y Hexomino that can be placed on a $13\times 13$ chessboard, where each Hexomino does not overlap?
From the ...
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Shadow shape of cube
Imagine a cube on a flat table, tantalizingly balanced on one of its vertices such that the vertex most distant from it is vertically above it. What will be the projection on the table if there is a ...
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Expected value with unit cubes and random lines
I am trying to solve this month's Jane Street puzzle in which there is a 3-space partitioned into unit cubes and a line of length D is randomly chosen uniformly in location and orientation. I want to ...
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The set of points covered by a bouncing ball
I wonder in which condition a bouncing ball can cover every point in the set $[0, 1]^2$.
Problem statement:
Given a straight line $l$ on $\mathbb{R}^2$. Let
$$
C = \{(x - \lfloor x \rfloor, y - \...
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2
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Last Ball Brain Teaser Question
A bag has 20 blue balls and 14 red balls. Each time you randomly take two balls out.
(Assume each ball in the bag has equal probability of being taken). You do not put these
two balls back. Instead, ...
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What day(s) of the week cannot be the first day of a century non leap-year that is a perfect square?
This question is from contest our in school:
What day(s) of the week cannot be the first day of a century non-leap year that is a perfect square year?
My attempt
A Century year is a non-leap year ...
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0
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73
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Domain of the biggest value for $abcd\dots$ given $a+b+c+d\cdots=10$
I've seen this puzzle on Flammable Maths new video (https://www.youtube.com/watch?v=vW4TjU4IoPY)(optional to watch). It is as follows:
"Given a+b+c+d+e...=10, what is the biggest value for abcde.....
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1
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1
answer
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Is there solution to this problem of cosine of difference of angles?
Consider this equation
$$ e =\left(\cos \left({\frac{A - B}{2}}\right)\right)^{2} $$
Is there a solution for functions $f$ and $g$ such that
$$e = \frac{f(A)}{g(B)}$$
The initial application of ...
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votes
1
answer
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Lightbulb riddle
Suppose you have $n$ lightbulbs evenly distributed over a circle. Each lightbulb can have two states; it's either turned on or turned off. Next to each lightbulb there is a button that changes the ...
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The toys problem: Probability of getting two matching good item and a different third Item
I've encountered an intriguing probability problem. I just registered to ask this, so this will be my first post.
Disclaimer: I met this problem in a real setting that's it too convoluted to explain (...
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What are way to represent Zebra(Einstein) Puzzle mathematical or formal form
I look how to implement the algorithm (program) for solving so called Zebra(Einstein) Puzzle.
For that, i look for some formal or mathematical representation of conditions in this puzzle.
Can you ...
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68
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find the shaded numbers that make a grid puzzle ready and complete the puzzle
A 5 by 5 Latin Square is a 5 by 5 grid of squares in which each square contains one of the numbers 1 through 5 so that every number appears exactly once in each row and column. A partially completed ...
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1
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Placing the $21$ two-digit primes into a grid, such that primes in adjacent squares have either the same tens digit or ones digit
This is USAMTS round 3, problem 1 of the 2020-2021 Academic Year.
Place the 21 2-digit prime numbers in the white squares of the grid on the right so that each two-digit prime is used exactly once. ...
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1
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Minimum swaps to put an array into desired order, where some elements are identical/repeated
Inspired by a word game Waffle, see footnotes if interested. The abstracted problem:
You're given an input array of letters, some of which might be identical (i.e. repeated), e.g. ...
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votes
1
answer
49
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Jigsaw puzzle ratio question.
I was doing a puzzle when this question popped into my head:
Assuming a puzzle had an equal amount of pieces in each row, and an equal amount of pieces in each column, what would be the least amount ...
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votes
0
answers
94
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Expected time until you reach the top of staircase in a dice game
I received this question during an online assessment and it continues to bug me. The setup is the following: you have a staircase with $100$ stairs in front of you, and at each time step $t$ you roll ...
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0
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105
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Fox and rabbit on circular path
Thank you for your solutions "Can fox catch rabbit" (There are five holes in a line. One of them is occupied by a rabbit. Each night, the rabbit moves to a neighboring hole, either to the ...
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1
answer
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Finding defected boxes puzzle
If I have say $6$ boxes of marbles such that each of the box contains $100$ marbles each of which weigh $1$ gram. Now I get a call from my marble dealer saying that there is a chance that any of the ...
- 561
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1
answer
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100 prisoners riddle - Dependency of probabilities
I am referring to the well-known riddle of the title (if you don't know what I am talking about here it is: https://en.wikipedia.org/wiki/100_prisoners_problem - See sections "Problem" and &...
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1
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56
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Logical Puzzle - finding pattern
My attempt:-
Two pairs of cells :- (c1,c3) and (c1,c2); therefore, c1+c3=c1+c2 or c2=c3=x
Similary, another two pairs of cells I took were :- (c4,c5) and (c4,c6) with common cell having 5 in it, I ...
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