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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9
votes
5answers
2k views

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 ...
20
votes
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 ...
5
votes
2answers
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 $n$ ...
6
votes
2answers
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 ...
8
votes
2answers
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 ...
2
votes
1answer
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 ...
5
votes
1answer
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 ...
7
votes
17answers
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 ...
13
votes
3answers
1k views

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 ...
10
votes
5answers
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 ...
6
votes
2answers
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 ...
12
votes
5answers
1k views

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. ...
3
votes
3answers
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, $4$. (...
4
votes
4answers
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 ...
4
votes
10answers
5k views

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:
27
votes
19answers
6k views

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 ...
6
votes
1answer
507 views

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 ...
10
votes
4answers
9k views

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 ...
6
votes
2answers
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 ...
32
votes
16answers
6k views

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 ...
1
vote
4answers
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 ...
19
votes
2answers
2k views

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 ...
25
votes
7answers
3k views

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 ...
6
votes
3answers
700 views

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 ...
0
votes
2answers
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 ...
8
votes
2answers
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 ...
2
votes
1answer
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, ...
14
votes
3answers
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 ...
14
votes
5answers
2k views

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 ...
3
votes
1answer
1k views

Alphabet Number Matching

If : 888888 = T 777777 = O 555555 = Y 444444 = R then : 666666 = ? Basically you need to tell the logic along with ...
1
vote
1answer
254 views

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 $x\times y = 941121$.
3
votes
1answer
1k views

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 ...
4
votes
1answer
395 views

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:
7
votes
2answers
3k views

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 ...
5
votes
2answers
1k views

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 ...
12
votes
6answers
7k views

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 ...
3
votes
1answer
520 views

Evaluate the long multiplication

Evaluate Q1:$[-100\times (-99)] \times [-99 \times (-98)] \times [-98 \times (-97)]..... (97\times 98)\times (98 \times 99) \times (99 \times 100)$ And Evaluate Q2:$(-100-98) \times (-99-97) \...
4
votes
3answers
414 views

$n$ monsters and $n$ people

There are $n$ monsters (M) and $n$ people (P) on the left side of a river. Nobody is on the right. They have a boat that can hold up to 2 beings. At no point on time may either of these be true: $$M_{...
10
votes
1answer
292 views

Blessings of Ares

Two gladiators are about to do battle in the coliseum. Before the battle, they enter separate rooms and pray to Ares, the god of war. Ares blesses them each with random amount of power, which you can ...
-2
votes
1answer
2k views

Calculating row number and column number [closed]

What I am trying to do is calculate the row and column of which an id is in. For example I have the grid 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 As you ...
-1
votes
1answer
530 views

A Hunter wants to get on a Bus [duplicate]

A hunter wants to get on a bus, but belongings which have larger than 1 meter dimensions is not allowed. So how will he be able to get his rifle (which is 1.5 meters) together with him without ...
-3
votes
2answers
136 views

Points following an axiom [closed]

Your aim: Mark any finite number of points on a plane. It should meet this axiom. Axiom: Original way of stating it: If a line (infinite) is drawn passing through exactly n (n>0) points, any line ...
13
votes
1answer
1k views

A Quote from what Movie?

Heads up: It's possible to solve this puzzle without writing computer code, but it is intended to be solved with computer help. This is a 2-stage puzzle. Stage 1: Calculation Puzzle Rules: 1. You ...
18
votes
6answers
2k views

Pursuit Problem: Mutineer trapped on an island

You are a pirate. One of your crew ran off in the night, swam to your secret island, and dug up your life's treasure. You need to capture her. You may deploy $n$ pirate ships to patrol the boundary ...
12
votes
4answers
830 views

Pursuit Problem II: Surrounded in Marauders' Circular Cove

(This is the sequel to this puzzle. It has a similar setup, but believe me, the solution is very different. Be careful! The answer is counterintuitive. It shocked me at first.) You are a pirate. ...
4
votes
1answer
322 views

Mathematical probability with cards

A box contains 900 cards enumerated from 100 to 999 (Each number appears once and just in one card). I took some random cards without looking at them and calculated the additions of the digits in each ...
17
votes
2answers
2k views

Game of Drones - Zap it!

Your programmable drone is pitted against another drone in a rectangular 3D arena measuring 40 meters long, 40 meters wide and 20 meters high. You have equipped your drone with a laser gun that will ...
20
votes
3answers
6k views

The lake monster

You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can't swim. He can run (along the perimeter)...
3
votes
3answers
292 views

Repunit replication

Repunit is a number consisting only of $1$s (here in base $10$). Examples - $1$, $11$, $11111$. Goal Create 10 first repunits $n$-digits long from least possible number instances of numbers $n$. ...
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 ...

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