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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19
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4answers
1k views

The frog concerto

A pond contains $24$ waterlilies that are arranged in a rectangular $2\times12$ grid (that is, two rows with twelve waterlilies). One evening $24$ frogs give a croaking concerto for the residents of ...
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9answers
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Perfect Squares!

A question was asked in a mental ability test yesterday. Write four distinct numbers with these properties: 1. Sum of each pair is a perfect square. 2. Sum of all four is also a perfect ...
12
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2answers
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How to ship the new Slurm 7-pack efficiently

The six-pack is a thing of the past. Beverages of the future will use the seven-pack format. But how will the mighty spacemen of the future manage to ship the Slurm seven-pack efficiently in ...
8
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1answer
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Can you pass through the ancient tomb? Find the correct interpretation for the symbols

You have been crossing this hot and wet place for weeks now, but when you enter the cool and mouldy ruin, you know in seconds it has been worth it. Nobody has ever been here ( - well nobody in last ...
5
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2answers
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If you choose an answer to this question at random, what is the chance you will be correct? [closed]

If you choose an answer to this question at random, what is the chance you will be correct? A) 25% B) 50% C) 60% D) 25%
27
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5answers
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First odd number in a “number dictionary”

All numbers between 1 and 1010 are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "onethousandtwentyfour". Also, "...
26
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2answers
2k views

Mathematical Rebus II

Mathematical Rebus I Mathematical Rebus III $$\det\frac{\partial(x,y)}{\partial(r,\varphi)}\\ \sum_{n=2}^\infty \ddot{\frac{t^n}{n!}} $$
23
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8answers
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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
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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
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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. ...
9
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1answer
532 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 ...
5
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2answers
531 views

Paint 7 cells of a 7x7 grid

Can you paint 7 cells of a 7x7 grid such that the largest unpainted rectangle has area of 6 cells? Good luck!
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5answers
959 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
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9answers
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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
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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 ...
19
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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
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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....
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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
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5answers
668 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 ...
9
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1answer
2k views

Three button calculator

A calculator has only 3 buttons. The first multiplies the current value by 3, the second adds 2 and the third subtracts 2. Starting with 0 what is the least number of presses you need to reach 100?
7
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4answers
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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
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5answers
281 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
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1answer
565 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
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2answers
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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
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3answers
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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 ...
22
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10answers
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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
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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 ...
16
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3answers
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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 ...
11
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1answer
391 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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5answers
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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
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2answers
277 views

Teacup geometry

Inspired by the three utilities puzzle from prog_SAHIL I'm now posting a similar puzzle that makes use of the topology of a cup with a handle: The question is: How many distinct points can you ...
7
votes
1answer
933 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
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2answers
850 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 ...
7
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2answers
625 views

Peaceable Bishops on an 8x8 grid

Place an equal number of red, white and black bishops on a 8x8 chess grid, such that no two bishops of different colours attack each other. What is the largest number of bishops you can place? Bonus ...
5
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1answer
616 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
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4answers
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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, ...
5
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1answer
554 views

The Minotaur's Labyrinth

You are trapped in a chamber in the center of the Minotaur's Labyrinth. There are $\mathbf{N}$ tunnels, $\mathbf{m}$ of which lead to safety; the remaining tunnels only lead back to the chamber. Each ...
0
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2answers
354 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. ...
-1
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3answers
922 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
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7answers
6k 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
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1answer
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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: ...
15
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3answers
3k 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 ...
13
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5answers
635 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 (...
13
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2answers
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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
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1answer
540 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 ...
11
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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
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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 ...