Questions tagged [mathematics]

A puzzle strongly related to mathematical facts and objects, or whose solution needs serious mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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23
votes
8answers
3k views

How to choose at least half of everything

Some number of gold, silver, and copper coins are scattered in $N$ chests. You may look into each chest and count each type of coin in them, and then select $M$ of the chests. Your goal is to have at ...
20
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2answers
1k views

The Faulty Keypad Safe

Acme has released a brand new safe, secured with electronic 10-button keypad with the digits 0 through 9, with an X-length combination required to unlock. However, due to laziness, the keypad's ...
17
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3answers
2k views

Baggage Problem: $1.5$-meter-long sword onto a train

This is the problem I came across reading the book The Art and Craft of Problem Solving. When I read this question I wasn't able to figure out the solution and I saw the solution after a while, but ...
14
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1answer
2k views

A classical combinatorial puzzle

It is a classical puzzle by Edsger Dijkstra. Not quoting the original problem but changing it into bag and balls, the puzzle is: A bag contains some black and white balls. The following process is ...
13
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2answers
2k views

The last number on the blackboard

The numbers $ 1, 2, \ldots, 500 $ are written on a blackboard. Each minute any two numbers are wiped out and their positive difference is written instead. At the end only one number remains. Which ...
12
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2answers
1k views

Escaping a hungry lion you can't outrun

You are at the edge of an enormous circular arena. A hungry lion is eying you from the centre of this area. You are both capable of running at the same maximum speed, but constraint within the arena. ...
11
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6answers
1k views

A problem circularly coined

I have two coins - one has $N$ times the diameter of the other. I roll the smaller coin one full lap around the circumference of the larger coin like a gear, keeping contact it in with the edge of the ...
9
votes
1answer
525 views

Two students guessing positive integer

Q. Two students A and B think of a positive integer. They tell the teacher their positive integer, but they don't tell each other their positive integer. The teacher tells both of them two different ...
1
vote
5answers
946 views

Obi-Wan vs Grievous

19 BBY, the Galactic Republic spots General Grievous in Utapau, the Separatists' Council Base; the Jedi Obi-Wan Kenobi is sent there to deal with him. After a long search, Obi-Wan comes face to face ...
34
votes
9answers
5k views

Can political debates really work?

In the far-off country of Politica, there are three main parties: the Left, the Right, and the Centre. In the last election, there were 19 million Left voters, 21 million Right voters, and 23 million ...
20
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4answers
5k views

Infinitely many dwarves wearing hats of 2 colours

I have heard of the puzzle with 100 or 10 dwarves wearing a hat of a color, either red or blue, and standing in a straight line, and having to guess the color of their own hat - it's quite easy. The ...
18
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5answers
1k views

The Computer Science Department

On a tour of a nearby university, we went into the computer science department. I was fascinated by the courses they offered, of course, but there were weird grids displayed on screens along the ...
15
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3answers
2k views

The clearly wrong proof

Bob claims to have a proof that $0.\dot1=1$. That's $0.\overline1=1$, $0.(1)=1$ or $0.11111...=1$ in other common formats. The proof starts $$\text{If }1x=0.\dot1,\\ \text{then }10x=1.\dot1\\ 10x-1x=1....
10
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2answers
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The three utilities puzzle

Here is a variant of the three utilities puzzle. Famously, It is impossible to solve it on a plane paper (Euler's theorem can prove that). But can you solve it on a coffee mug? ...
9
votes
5answers
664 views

Wolves and a Hare on a tiny planet

On a tiny spherical planet there exist $N$ wolves and 1 hare. The planet is so small any of these creatures can circle it in exactly 1 day. No creature needs to sleep or eat. The wolves communicate ...
7
votes
4answers
2k views

Dr. and Mrs. Smith shake some hands

Dr. and Mrs. Smith recently attended a party at which there were 5 other couples. Various handshakes took place. No one shook hands with his/her spouse, no one shook his/her own hand. After all the ...
6
votes
5answers
274 views

Halve or diminish, and race to unity!

Alice and Bob are playing a game. In the beginning, the integer $9172016$ is written on a blackboard. In a move, a player, can: either decrease the number on the board by $1$ (i.e., replace $n$ by $n-...
5
votes
1answer
560 views

Find the smallest N to complete the task: “Write a true self-reflective statement about the digits from 0 to N”

Following this question, consider the case where we change the number of digits and formulate the task like this: Write the statement like "This statement contains $M_0$ 0's, $M_1$ 1, ..., $M_N$ N'...
5
votes
2answers
3k views

Finding the number of ways of crossing a river

There are $X$ stones in the river.The stones are placed in such a way that a person can jump from one stone to the next one, or skip one and jump to the one after that. Find the number of ways in ...
4
votes
3answers
951 views

Total no of squares on a Chess Board

Is there any formula than calculates the total number of squares on chessboard? For example in a $8\times8$ chessboard, there are squares of sizes $1\times1$, $2\times2$, $\ldots$, $8\times8$. So I ...
3
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6answers
40k views

Fill number in missing?

Given options are: A. 13 B. 42 C. 18 D. 30
22
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10answers
6k views

How many diamonds? [duplicate]

A group of Seven men robbed a diamond shop at night. They ran to a nearby forest and all slept there for the night. One of them woke up and tried to run away with the bag full of diamonds, but ...
16
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3answers
2k views

A knockout tournament

$12345$ players take part in a knockout tournament. In each round players are paired up; each pair plays a game with the winning player advancing to the next round (no ties). If there are an odd ...
16
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3answers
3k views

A clock where the hour and minute hands are the same length

Your buddy Frankie sold you a shoddy clock: it keeps good time, but the minute and hour hands look exactly the same! Both of these hands move continuously, and there is no second hand. How many times ...
11
votes
1answer
387 views

The adventitious 18-gon

Today I have drawn a regular $18$-gon on a piece of paper. My drawing shows the $18$ vertices of the polygon labeled as $P_1,P_2,\ldots,P_{18}$ in clockwise order, and it also shows all $135$ ...
8
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3answers
4k views

How can 12 teams rotate through 6 games without overlaps?

Given the following: Six Number Teams (1 - 6) Six Letter Teams (A - F) Six Games (Basketball, Football, Baseball, Volleyball, Hockey, Rugby) Six Time Slots (1pm - 6pm) Set up a game schedule that ...
7
votes
5answers
16k views

Meeting of hands on a clock

We have a regular analog clock with three hands - second, minute and hour. On a given day, how many times do: (a) the minute and hour hands (b) the minute and second hands (c) the hour and second ...
7
votes
1answer
900 views

On 8x8 board, a knight is on the second square of the last row. Only moving upwards, how many routes to the top?

In chess, a knight moves in L-shaped jumps consisting of two square along a row or column plus one square at a right angle. It can only move upwards. How many routes can it take to any square on the ...
7
votes
2answers
814 views

Triangle with incircle [closed]

This question is from the German mathematics competition Känguru der Mathematik. In this competition students have to solve 30 mathematical tasks like this in 90 minutes without calculator. Actually ...
5
votes
1answer
607 views

Pythagorean coins

To make payments, the Pythagoreans use coins in no more than three denominations. The three denominations are in whole Oboloi amounts, and the sum of the squares of the two smaller denominations ...
5
votes
4answers
1k views

Making 1-50 from 2016

Make the numbers 1-50 using the numbers 2 0 1 6 in the given order. 1.You must use all four digits. 2.You may not use any other numbers. 3.You may use +, -, x, ÷, square root, squaring and cubing, ...
0
votes
2answers
353 views

Cops - The ultimate compass challenge [closed]

Based on The square and the compass This is a new kind of challenge proposed on Meta Puzzling SE. Any discussion about the general type of puzzle (rather than this particular one) can be done there. ...
0
votes
3answers
895 views

Inheritance by cards [duplicate]

An old farmer passes away in his sleep. After a suitable period of mourning, his three sons find their father's will in his study. Amongst other, simpler bequests is the following: "I wish my small ...
-1
votes
7answers
5k views

How fast can you solve this?

I posted this to compare times with individuals that possess intellects lightyears beyond my own. I clocked in at 16 mins for this answer. I know my time will be overtaken by a time that's less than ...
15
votes
3answers
2k views

Temple lake question

There is a flower garden, a lake and three temples. If we throw a flower into the lake, we will get back triple the number of flowers we threw in. A man wants to keep an equal number of flowers in all ...
15
votes
1answer
1k views

Rybo switched the calculator keys!

I'm Dave. In revenge for my calculator key-switching prank, Rybo has performed a similar prank on me! My calculator has the usual number keys, and keys for the usual four arithmetic operations: ...
13
votes
2answers
1k views

The barge ladder

You are the captain of a large barge and need to cross a canal in order to transport your barge from the sea to a lake above sea-level. As you probably know, when you enter the lock, water is added ...
12
votes
1answer
510 views

Enlarge the Square?

There are four stones, positioned on the ground at the vertices of a square. At any time, you may pick up a stone and "hop" it over another one so that it lands an equal distance beyond the hopped ...
12
votes
5answers
547 views

Labelling a Snow Flake Graph to Attain Minimum Sum

Label the vertices (or nodes) of this graph with positive integers so that any two nodes are joined by a edge (or line) if and only if the corresponding integers have a common divisor greater than 1 (...
11
votes
1answer
1k views

Star-Lord and the Space Police

Star-Lord is on a deserted planet along with two space policemen. If he runs into either of them, he will get immediately arrested. Fortunately for Star-Lord, somewhere on two opposite ends of the ...
10
votes
2answers
3k views

How many Strobogrammatic numbers are there from 0 to 99999

0,1,2,5,8,11,69,96 are Strobogrammatic numbers. We call a Strobogrammatic numbers if: When it is typed on a calculator, and the calculator is spun 180 degrees, the number visually looks the ...
9
votes
3answers
3k views

$n$ couples crossing a river

There are $n$ couples on one side of the river. Nobody is on the other side. They have a boat that accommodates up to 2 people. For every trip across, someone(s) must bring the boat back as well. The ...
7
votes
3answers
882 views

Spreading Gossip

Initially, each of 50 Puzzling Stack Exchange users have a single distinct juicy bit of gossip not known to the others. If $A$ sends an email to $B$, that email can include all the bits of gossip $...
7
votes
4answers
283 views

Savage Road Signs (Part 2)

Please read part 1 or this might be confusing Since part 1, you have replaced the stolen stickers and your daughter has forgiven you. The highway ended up being a full 700km long, so you are happy ...
7
votes
4answers
2k views

A truly amazing way of making every possible positive integer

This is a follow-up to "A truly amazing way of making the number 2016": For every positive integer $n$, find a mathematical expression that yields the value $n$ while obeying the following rules:...
7
votes
1answer
953 views

Probability of Seeing a Car in 10 Minutes & 30 Minutes [closed]

On a deserted road, the probability of observing a car during a thirty-minute period is 95%. What is the chance of observing a car in a ten-minute period? Hint: To clarify the question we are saying ...
6
votes
1answer
131 views

The town of Concentrië

Here you see a water map of the town of Concentrië. There are eight channels that run from the central boathouse of the city in a star shape. There are three canals that lie concentric around the ...
6
votes
3answers
2k views

Coloring an n by n grid with four colors

This is a generalization of Place 4x12 detainees on a 7x7 grid of cells. The goal is to color the squares of an $n\times n$ grid with four colors such that at most one square is uncolored no two ...
6
votes
3answers
717 views

Mathematical Rebus III

Mathematical Rebus I Mathematical Rebus II Small note on the first image: Hint 1 for the squares image: Hint 2 for the squares image: Hint 3 for the squares image (alternative image that should ...
6
votes
1answer
481 views

The square and the compass

(I don't mean $x^2$ or $N\cdot S\cdot E\cdot W$) You have a compass and a pencil but no scale/straightedge. Your job is to mark four points on a plane paper that would form a square if joined. Your ...