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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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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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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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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An Evolutionary Experiment

Dr. Farnsworth entered class today and announced that we were going to conduct an experiment to see if we could force cells to evolve to communicate with us. The experiment is as follows: we are given ...
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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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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 ...
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Welcome to Oɴᴇderland

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...
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The PSE School of Enigmatics (Part 1)

Update: I fixed up the second image, making it (perhaps) a little bit easier to crack. You leap out of your bed. Today's the day! You check your mailbox, and wow, there it is! The frayed look of the ...
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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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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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Make numbers 1 - 30 using the digits 2, 0, 1, 8

It's 2018 so let's repeat last year's challenge with new digits. This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 8. Rules: Use all four digits exactly once Allowed ...
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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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A COVID-19 puzzle: How large a class do you need to fit 30 pupils?

Some countries are proposing to reopen high schools soon. To ensure safety, they want to make sure that all pupils in a class are at least 2 m apart. To help them find the smallest room that can ...
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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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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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Four points with only two distances

Your task is this: Find all arrangements of four distinct points in the plane such that only two distances occur between them. When you have $4$ distinct points, you can measure the distance ...
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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 ...
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Variation of 100 prisoners light problem

There is a classic problem below for which Dr. Yisong Song wrote a very well written and thought out series of solutions. The variation here I've never seen anywhere but am curious. I want to work it ...
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558 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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How much money can we make?

My five friends and I used to loan each other money all the time. But over the past several years we have moved apart. We don't trust PayPal, banks, or the postal service so transferring money over ...
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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 ...
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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)...
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A rectangular room has a floor tiled with tiles of two shapes: 1×4 and 2×2

A rectangular room has a floor tiled with tiles of two shapes: 1×4 and 2×2. The tiles completely cover the floor of the room, and no tile has been damaged, or cut in half. One day, a heavy object is ...
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Get 100 as an answer on a calculator without using 0

Task Get 100 as an answer with only four keystrokes on a regular calculator. Disallowed keys 0 00 Allowed keys All other than the aforementioned two keys. Take the below image as a reference. ...
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The 100 soldier problem

I saw this problem many years ago. I am sure many puzzlers will know its original name. I was reminded of it when reading about Conquering of Regions problem. A Strategy Game Involving Conquering of ...
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Which data file is genuine?

NASA has spent hundreds of millions of dollars gathering data about cave systems in one region of the planet Mars. The project just finished up, and analysts will soon be ready to start analyzing the ...
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Musical in Nature

What is the next song in the list? Pedal To The Medal Not Inside -- Outside The Final Countdown Every Rose Has Its Thorn ......... The Puzzle Within these dots, you shall find a magical, mystical, ...
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Gambling in a rigged casino

A well-known crooked casino is offering the following bet with a pair of (identically looking and indistinguishable) dice that both show the numbers $1,2,3,4,5,6$ on their faces. The first die ...
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The life of a Knight: Conway style

So I was thinking about Conway's game of life and the ridiculous kinds of patterns that can be made (Things that move across infinite space etc) and then I thought, hey could a chess knight do this as ...
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Make 5 5 5 5 = 19 [closed]

Can you find a way to make: $5\ 5 \ 5 \ 5 = 19$ by adding any operations or symbols? You can use only these symbols: $+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$. It is limited to this list, and ...
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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 ...
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Google's 20th Anniversary: Make 20 using 6 0 0 6 1 3

Belated 20th Happy Birthday to Google (600613)! Challenge: Use 6, 0, 0, 6, 1, 3 to make the number 20. Rules: Use all numbers, in that exact order. Allowed operations: +, -, x, /, sqrt, (); no ...
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A magic trick of David Copperfield

David Copperfield puts $52$ cards numbered $1$ to $52$ into three top hats. One of these top hats is red, one is blue and one is yellow, and each of them receives at least one card. Then David ...
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The Monty Hall problem

I'm amazed that, although well known, this problem hasn't been posted yet. Monty Hall You are on a game show. The host of the show shows you three doors. He tells you that behind one of them, is a ...
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How many flowers to buy? [duplicate]

A man decided to place some flowers on three different temples. There is a magical pond before each temple and he has to swim through each one. So his trip will be: [ pond1 - temple1 - pond2 -...
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Digging a tunnel between random locations

Romeo and Juliet are each placed uniformly at random locations on a spherical planet, meaning that each square meter of surface area of the planet is equally likely. Romeo decides to dig a straight-...
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Worm and an Apple

Johnny has a perfectly spherical apple, with a diameter of 70 mm. While he looks away, a worm burrows through (entering and leaving) the apple, forming a single tunnel of length 69 mm and negligible ...
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A game with 52 cards

Alice and Bob play the following game with two (identical) standard decks of $52$ cards. First Alice secretly arranges one deck of $52$ cards in a long row on the table. All cards are face-down, and ...
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How much water do you need to cross the desert?

This question is inspired by Terry Pratchett's "Small Gods," in which an army crosses a vast desert by making multiple trips and caching water along the way. 1. Provide an answer. 2. I doubt I'm the ...
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bored of eating soup

A man orders spicy noodle and leek soup from a restaurant, but gets bored while eating. When he gets bored, there are exactly 100 noodles in the soup. Because he is bored, he decides to play a game ...
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The year 2016 is approaching

Do there exist integers $r,s,t\ge100$ such that the decimal representation of $(r+\sqrt{s})^t$ is of the form $~~~\ldots\ldots2015\,.\,2016\ldots\ldots$? (In other words: the four digits before the ...
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The LoL number game

Tim and Tom are fictional characters (cats, I believe) who like to play the LoL number game. In this game, Tim chooses two distinct integers A and B, both ≥ 2, and shows them to Tom. Tom's goal is to ...
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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 ...
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3 Numbers on Hats, A = B + C

This feels like it should be a common puzzle, but I haven't found anything exactly like it searching online, so here goes. Apologies if it's a duplicate. Three logicians, person 1, 2, and 3, along ...
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A few Mathematicians derived from formulae

Find the 3 mathematicians which may be revealed, with a little manipulation, from the formulae below. They are well known enough to be in the MacTutor History of Mathematics archive. $$\frac{\chi }{...
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Powers of two my children be

Powers of two my children be, Arriving in birth years separately. Their sum is now the reverse of me And the years between me and a power of three. My digit difference is the number ...
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Ernie's Clockwork Calculator

I was helping Ernie clean out his shed a while back when I saw a curious old machine. "Oh yeah, that!" said Ernie, when I pointed it out to him. "A few years back, before transistors were invented, I ...
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The answers to these questions are?

C is the correct answer to how many questions? A. 1 B. 2 C. 3 D. 4 Which letter is the correct answer fewer times than any other? A. D B. B C. C D. A Which letter is the ...
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Five Angles in a Star

In a regular pentagram (5-pointed star), the angle in each point is 36 degrees, so the angles in all five points sum to 180 degrees: What about an irregular pentagram, such as the following? Now the ...
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Picking up stones

Here is puzzle that was lifted from an old essay of mine, that was adapted from a puzzle in an old puzzle book. The great shah has invited a young boy into his palace as a student. While he is not ...

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