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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Noughty Mathematics Question

Use your imagination to follow these instructions: Take out an imaginary piece of paper. Turn it 90° clockwise. Make a mental note to use right-justification and nice, tight kerning and leading. In ...
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9answers
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How many steps are visible on the Escalator?

Alice walks down an upward escalator and counts 150 steps. Bob walks up the same escalator and counts 75 steps. Alice takes three times as many steps in a given time as Bob. How many steps are ...
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A lonely pawn on the chessboard

Alice and Bob and the referee Conny play the following game with a pawn on a standard $8\times8$ chessboard: In the beginning, Conny places the pawn into the center of a randomly chosen square. All $...
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3answers
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Can you see out of the forest?

You are standing at the centre of a circular forest of radius 500 metres. The trees of this very regularly planted forest stand in a precise rectangular lattice on the plane, each 10 metres from the ...
27
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19answers
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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 ...
27
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5answers
710 views

Dissecting the holey octomino into a square

This is a pure dissection problem, with no added twists. Cut the holey octomino (i.e., a square with the middle third removed) into several pieces, and reassemble those pieces into a square with no ...
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, "...
27
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9answers
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Winnie-the-Pooh and the 27 honey pots

Winnie-the-Pooh keeps his $27$ honey pots in the larder. Each pot contains up to $1$ kilogram of honey, and different pots contain different quantities of honey. All $27$ pots together contain $17$ ...
27
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3answers
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Maximum time for ants to fall off stick

Suppose there are $n$ ants on a stick which has length 1. At any time, the ants may be facing left or right, the initial directions of the ants are arbitrary. Each ant can be modeled as a point in the ...
27
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1answer
2k views

Just do it rebus

$\Large n = \Large a^{-1}\cdot e^{\frac{\huge it}{\huge s}}$ It is a catchy phrase.
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10answers
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One prize, infinitely many choices

Having reached the final stage of a game show, you face an endless row of doors labelled $1$, $2$, $3$, ... The game show host has selected a whole dollar amount, and has put this exact amount as a ...
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3answers
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Numbers on the blackboard: From 2-2015 to 1-2014

The numbers $ 2, \ldots, 2015 $ are written on a blackboard. Each minute any two numbers $ x $ and $ y $ are wiped out and are replaced by two numbers $\displaystyle \frac { 4x + 3y } { 5 } $ and $...
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A clock for 2017

Design a clock where each number from 1 to 12 is obtained as an arithmetical operation using each digit of 2017 exactly once: for example, 4 could be made as $2\times 7-10$.
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7answers
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What's the perimeter of the hexagon?

Consider a hexagon which is equiangular but not equilateral: all angles equal to 120 degrees but four consecutive sides of length $a,b,c,d$ not necessarily equal. What is the perimeter of the hexagon? ...
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11answers
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Make 11 from five identical digits

At a tender age my father introduced me to an arithmetic game: making the number 11 from five single digits using only the basic operators listed here: ...
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3answers
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Finding digits that sum to 15

Rand and Rubio are playing a game in which they each take turns to pick a digit between 1 and 9, without replacement (i.e. all digits chosen are distinct). If one of them manages to get three digits ...
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3answers
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One hundred tiles

One hundred tiles are arranged in a $10 \times 10$ square. Each tile is black on one side and white on the other side. Two types of move are allowed: Flip over all four tiles in any $2 \times 2$ ...
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2answers
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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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5answers
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An unusual and very hard number sequence problem

I heard this number sequence problem about 25 years ago from a maths lecturer. What number should go in the place of the question mark in this mathematical sequence: $..., 30, ?, 60, 90, 140, 225, ...
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6answers
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Stargate escape

What a nightmare! When you awake in cold sweat you only remember dazzling colours, flash-lights, dark shadows with far too many arms and the sickening sensation of being dropped from a high place. ...
26
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3answers
810 views

Ever increasing highway numbers

A province has 10 cities (arranged in a circular manner). Every pair of cities is directly connected by a straight highway, and each has its own unique number: Highway 1, Highway 2, Highway 3, ..., ...
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1answer
3k views

The tough one from “A Brilliant Young Mind” (2014)

Great movie by the way. I'm quoting from memory, so I may get the wording wrong. The positive integers are each colored Red, Yellow or Green. Prove that for any such coloring, there must exist ...
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4answers
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This image contains a “Great Discovery”

The Puzzle: Source material taken from here As discussed on Numberphile, here is John Herschel's doodle, sent to his friend Charles Babbage. John H. John Herschel was an English polymath, ...
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11answers
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What is my four digit car number?

My car has a four digit number. Its last digit is double the first digit its middle two digits are the same its last two digits are double the first two digits What is my car's number? ...
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2answers
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Five loaves and the extra traveller

Two people are travelling together. One of them has three loaves of bread; the other one has two. At some point they stop to eat lunch. A third traveler that happens to walk by joins them. They split ...
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4answers
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Make the equation true by only drawing a single straight line

Fred has a puzzle. The instruction sheet, which is separate from the equation,simply says: "Make this equation true. You may ONLY draw ONE, PERFECTLY straight line". The equation is all alone on a ...
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7answers
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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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How do I convince my grandmother?

How do I convince my grandmother (who really hates mathematics) that there exist three positive integers $x,y,z$ that satisfy the equation $28x+30y+31z=3650$?
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2answers
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Two chessmasters at work

Viswanathan Anand plays a chess game against Magnus Carlsen. Anand plays white and Magnus plays black. They use a non-standard digital double chess clock that is counting up from zero (instead of the ...
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1answer
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Maths equation: 357568588-11 = ~357568584.858

Move one line and make this true: $357568588-11 = $ ~ $357568584.858...$ No cross through the "=" sign stuff. Hint:
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Rooks on a 15x15 chessboard

On a 15x15 chessboard there are 15 rooks that do not attack each other (via ordinary rook moves). Then each of the rooks makes one move like that of a knight. Is it possible that after all this is ...
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2answers
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Unknown weight of four identical objects

Four identical looking objects weigh 3oz, 5oz, 8oz and 11oz. You do not know which objects weigh what and they are too close in weight to tell by holding them. Using a balance scale, how can you ...
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4answers
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What is the most triangles you can make from a capital “H” and 3 straight lines?

So start with an upper case H, and then draw $3$ straight lines. What is the greatest number of closed triangles that you can form? For example: Note that triangles inside of triangles only count ...
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4answers
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Ernie and the Pirates of the Caribbean

A few weeks ago, I dropped in to see Ernie to ask if he was willing to look after the cat while I was on holiday in the Caribbean. “No problem.” he replied then showed me an old leather-covered book, ...
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1answer
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Careless smokers

Cosmo complains: "At the party yesterday at our place, some guys were smoking in our living room. This morning we detected that these careless smokers had burnt four holes into the carpet." Fredo: "...
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1answer
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How many silver marbles does Paul have?

Peter, Paul and Mary have between them 282 marbles. Though of the three friends, it is Peter who has the most marbles, he is the one with the fewest silver marbles, just the square root of the ...
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4answers
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Lions and Zebras on a Chess Board

The black knight is our lion chasing 8 white bishop zebras which can't capture. Can the zebras evade the lion forever, if team zebra positions all the pieces and has the first turn? Rules: The game ...
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3answers
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What, the answer isn't the No of the Yes is?

Doorknob knows exactly how to solve this, so I ask him to not answer this question. Well, here's the puzzle: No, an answer is the cube without A, No? The Yes is No. The squared answer, Yes, is to an ...
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10answers
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Make 2 dice out of 3 dice

This question was first posted by standupmaths on youtube: https://www.youtube.com/watch?v=xHh0ui5mi_E He already got some answers but I think this community can probably find a better answer. ...
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4answers
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Arrows on a Chessboard

I've taken an $n$ by $n$ chessboard and drawn an arrow on each square, pointing in one of the eight compass directions. I've done this in such a way that arrows in (orthogonally) adjacent squares ...
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6answers
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Chess at the 2020 Olympic Games

For the 2020 Olympic Games, the World Chess Federation asked the Olympic committee to include chess as official sport. The committee agreed under one condition: The Chess Federation must design a ...
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3answers
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Unsolved Mysteries: Magic Square of Squares

This is the first in what will hopefully be a series of Unsolved Mysteries posts. Note that this puzzle has no known solution, nor any proof that a solution is impossible. We will see how ...
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16answers
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The Golden Bird and The Ocean

The golden bird can only fly at 5 mph. That is the only way the bird can move. The bird must stop flying and rest its wings for 5 hours immediately after every hour of flying it does. That is the only ...
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8answers
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How many cubes can we fit in?

You have a bag with many 3x3 Rubik's cubes . After solving all but one of them, you decide to play a new game. You take the unsolved cube, and start placing solved ones around it. The question: What ...
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10answers
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Thirteen politicians

Yesterday evening there was a public discussion on TV that was dedicated to the upcoming elections. Thirteen politicians from the thirteen most important political parties participated in it. After ...
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4answers
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The largest integer made of 1,2,3,4

What is the largest integer $A$ that can be produced from the four digits $1,2,3,4$ subject to the following rules? Each of the digits $1,2,3,4$ is used exactly once. Juxtaposition of digits is ...
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2answers
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2017 is the 1st prime satisfying three conditions. What is the 2nd?

$2017$ is prime, and so is $(2017+1)/2=1009$. $2017$ can be written as $a^2 + b^4$: $2017 = 44^2 + 3^4 = 1936 + 81$. $2017 \equiv 2 \bmod 31$. What is the next prime (if any) that satisfies these ...
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2answers
471 views

The mysterious operation $\oplus$

We are given an operation $\oplus$ that is associative and commutative, has $0$ as a neutral element, and we know: $1/10 \oplus 1/6 = 5/29$ $1/6 \oplus 2/3 = 7/10 $ $1/5 \oplus 2/5 = 3/7 $ $1/4 \...
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4answers
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Savage Road Signs

There is a highway that starts in the city of Savage. You must must place distance marker signs on this highway for the outgoing traffic. According to highway code, there must be a distance marker ...
24
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1answer
777 views

Oh dear, oh my, how blatant

Looking at the Puzzling Stack Exchange recently, I found a surfeit of number sequence riddles that all look the same! I mean, there's no difference between any of them. I'm sick and tired of all these ...