Questions tagged [mathematics]

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

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Another one of those odd sequence puzzles

This is an interesting one. I will do the same thing that I usually do. After one week, a hint. After 2 weeks, a hint. After 3 weeks, an answer. I may change this system. What number goes in the ...
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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 ...
458 views

N people, N hat colors, and a One-Way Glass

This is a variant of this question, reproduced below: There are $n$ people, who will stand in a circle while a game master places a hat on each of their heads. The hats can each be one of $n$ ...
638 views

Snow White and the Secret Message (Secret Sharing Problem)

Snow White needs to send a message to Prince Charming. She considers telling this message to each of the Seven Dwarves, then sending them to deliver it to the Prince. However, the road to the castle ...
385 views

Bracing a Flexible Grid

Suppose that you build an $n$ by $n$ grid out of metal rods, joined at their ends in such a way that they can rotate about the joints. Below is the grid when $n=3$, along with an illustration of its ...
509 views

What does this mean?

What is the magic word? 011021042021011012012032012032014 Clues (Read, in order, one and re-think the problem): Five letter word 'A' equals 011051 Binary (Eight digit per) Compressed ...
397 views

First Contact With Aliens

There is a strange meteor that is caught by the Earth's gravitational pull. No one even notices it because it is so small it will simply burn up in the atmosphere -- but it doesn't. Instead, it ...
18k views

Measuring the amount of liquid in a container without a measuring tool [closed]

The Problem Let's say you are asked to measure the amount of liquid in a container, but you are not allowed to use any direct measuring tool (such as a balance, ruler, or anything of the sort). You ...
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eXtreme Nim: A Game With *Lots* of Pebbles

Two children are playing a game with several piles of rocks. Each turn they do the following: They choose some pile of rocks. They count how many rocks are in this - let this be $n$. We remove this ...
820 views

Houses in a grid

You are a city planner tasked with the placement of unit-square-sized houses in a rectangular-grid allotment, the size of which is up to you but must be as small as possible to save money. The number ...
533 views

Unsportsmanlike Aliens

It was the first meeting of the humans and the aliens, and things were going well: The humans and aliens had learned to understand each other's language and found that both were hoping for a peaceful ...
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99 Bags of Apples and Oranges

You have $99$ bags, each containing various numbers of apples and oranges. Prove that there exist $50$ bags among these which together contain at least half the apples and at least half the oranges. ...
460 views

Magic cutting squares with given sum

You meet a guy on the road. The following conversation follows: He: Let's play a game. Give me any natural number from $3$ to $10$. I'll call this number the grid size You: Okay, $4$. (...
429 views

Queue in the bank

Six men are queuing in the bank when the clerk decides to take a break for 10 minutes! Before leaving, he gives to the six men a numbered ticket, in the same order of the queue (ticket #1 to the first ...
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In what field does π²=2?

In what field does $\pi^2=2$, where $π$ is the ratio of the circumference of a circle to its diameter? Remember to think outside the box and that I am looking for a complete answer. Hint:
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Ant walking on a number line

An ant walks on a number line, starting at location $x=7$. Each second, it randomly moves one space either left ($-1$) or right ($+1$), with equal chance. At $x=0$ and $x=10$ are drops of honey; the ...
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Lights in the theatre

A play of Romeo and Juliet is being held in the theatre tonight, hundred of people have been waiting this moment for months. Many people are currently working hard in the theatre to adjust the final ...
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N balls and a scale

The question of twelve balls and a scale is probably the best-known example of the "find the ball of a different weight" problem. But does it generalize? Is there a general way to find a weighing ...
467 views

Twilight Zelda Guardian Puzzle

I'm playing a game (see here), and in it is a puzzle, which I've made a TIKZ graph seen below for illustration: $\hspace{2.5cm}$ There is one player. The player ($\mathscr{L}$) moves from node to ...
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Brothers, cousins, and foes - what am I?

I am one of many siblings in a great family. We are the most perfect of our race, Because each of us has a clear worst enemy. My foe - I know him well - is much like me, But we continually fight ...
239 views

More males or females [duplicate]

In a society (presumably Asian) where sons are preferred over daughters, couples adopt the following heuristic when reproducing: If the new-born is a daughter, try for a new child When the couple ...
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Ernie and the Alien Invasion

Yesterday I dropped in on Ernie to show off my new j-watch. Ernie wouldn't be impressed by instant wrist-mounted access to social media sites like me-tube, tweeter and farce-book so I thought I would ...
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The population of Barberland

The Barberland Institute of Trichodemographic Research has published the following results: Nobody in Barberland has more than 1,000,000 hairs. No two inhabitants of Barberland have the same number ...
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Ages of A and B (self-reference in past)

A says to B My age is twice of what your age was when I was of your age. B says to A If you add your current age to twice of your age when I was born, the answer is $63$. Assuming they both ...
177 views

Switches and numbers [duplicate]

You have a hundred, labeled, bulbs, turned off and a hundred, labeled, buttons. When you begin pressing the button nº1, all bulbs turn on. When you then press the button nº2 all pair bulbs, begining ...
923 views

Overlapping Gang Territories

There are $7$ gangs in (a greatly simplified version of) Los Angeles. Each of them claims half of Los Angeles as territory. Let's say a place is "hot" if a majority of gangs claim it. How small can ...
547 views

Slot Machine Challenge

Karen owns a restaurant/bar. She wants to attract more customers, and is building her own custom slot machine game, which she can use to give away free drinks or prizes. The more a customer spends, ...
514 views

Cross, Dot and Scalar Product

This puzzle may seem off topic; though the motivation and background is somewhat mathematically technical, its solution is purely combinatorial (and quite cute). In multivariable calculus, the main ...
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Who's favored in this dice game?

Alyson and Bethany decide to play a game involving a (standard six-sided) die. Alyson goes first, and rolls the die: if she rolls a 6, then she wins. Otherwise, Bethany takes the die and rolls until ...
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Alphabet Number Matching

If : 888888 = T 777777 = O 555555 = Y 444444 = R then : 666666 = ? Basically you need to tell the logic along with ...
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Are there two integers $x,y>1$ such that $x\times y$ is the number you get when reversing the digits of $x$?

Title pretty much says it all. For example, if $x=121149$, one needs to find an integer $y$ such that $x\times y = 941121$.
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The puzzle is to decrypt this encrypted text. (Cryptograms)

The Encrypted text is: 7q7f 93d4 6s03 8aua 3pn9 73wu 9l2l a1wx 8u52 9tld 6fhc axfx 8kn4 628q 4abk 314d 255s 5o5b 9cc1 5904 4sja aa1r 7fai apsw 80ph ai09 ejbs I am currently (at the time of posting ...
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A sequence of integers

Here is my sequence (finite): 19,499,12991,337787,8782467,228344156,5936948059,154360649539. You just have to figure out its logic. Hint:
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Find the age of the ship and of the boiler

Some years back I was travelling by a cargo ship from New Zealand to Tahiti. I was curious to look around the ship one day and in the boiler room I asked a man how old the ship was. He smiled and ...
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What is the maximum number of cities that can be destroyed?

As a commander of an army battalion, you have to plan the attack on some enemy cities which are connected by road-network. Before starting the attack, you have information about all the cities and ...
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Greatest Digital Clock Number, with a Twist!

7 segments make up a number, some visible, some invisible. Just like on a digital clock: 88:88 or 04:00: There are 2 vertical segments on both sides and 3 horizontal segments in the center. What's ...