# 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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### 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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### 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 ...
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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 ...
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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 ...
38k views

### 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%
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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, "...
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### Mathematical Rebus II

Mathematical Rebus I Mathematical Rebus III $$\det\frac{\partial(x,y)}{\partial(r,\varphi)}\\ \sum_{n=2}^\infty \ddot{\frac{t^n}{n!}}$$
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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 ...
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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 ...
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### 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 ...
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### 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 ...
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 ...
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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. ...
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 ...
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### 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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### 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 ...
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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 ...
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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 ...
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### 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 ...
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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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### 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? ...
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 ...
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### 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?
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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 ...
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### 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. ...
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 ...
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 ...
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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: ...
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### 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 ...
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 (...
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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 ...
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 ...