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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74
votes
15answers
14k views

Making π from 1 2 3 4 5 6 7 8 9

There have been two other questions here and here that are similar to this one, but this changes the rules up a little. Your job is to approximate $\pi$ using the sequence of digits (in order): 1 2 ...
44
votes
7answers
9k views

How many tries to roll a 6?

Suppose you roll a (fair, 6-sided, perfectly ordinary) die repeatedly until you roll a 6. As is well known, the expected (i.e., long-term average over many trials) number of rolls required is 6. Now ...
75
votes
10answers
18k views

10 Prisoners, 10 Keys, and 7 Years

One day, the warden of a prison is, like most wardens in puzzles, feeling a little bit capricious and decides that he wants to get rid of his prisoners, one way or another. He gathers all the ...
33
votes
11answers
3k views

Coin weighing with a single weighing device

You have 12 coins which each weigh either 20 grams or 10 grams. Each is labelled from 1 to 12 so you can tell the coins apart. You have one weighing device as well. At each turn you can put as many ...
34
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 ...
28
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3answers
3k views

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 ...
63
votes
24answers
21k views

Make 0 0 0 0 = 8

Can you find a way to make: $0\ 0 \ 0 \ 0 = 8$ by adding any operations or symbols? You can use only these symbols: $+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$. It is limited to this list, and ...
56
votes
12answers
18k views

XOR - Is it possible to get a, b, c from a⊕b, b⊕c, a⊕c?

Just got a simple question from a friend; still thinking. Let's share it! Is it possible to get a, b, c when you have a⊕b, b⊕c, a⊕c ? where ⊕ is the boolean ...
42
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2answers
5k views

Ten numbers on a blackboard

The numbers 1 through 10 are written on a blackboard. You erase two numbers of your choice, and write their product plus their sum $$a,b \to ab+a+b$$ So, now there are nine numbers on the board. You ...
27
votes
10answers
3k views

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 ...
15
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6answers
721 views

A triangular Quidditch field

A Quidditch field is usually in the shape of an oval, a hundred and eighty feet wide and five hundred feet long. But today the Gryffindor house team is training on a smaller field in the shape of a ...
61
votes
8answers
17k views

A walk of 3000 meters, but one foot has moved more, how so?

My math teacher has struck again. Here's his newest riddle: Today I went for a normal walk of 3000 meters. One of my feet had to move exactly 3000 meters. However, the second foot moved 3100 ...
36
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6answers
3k views

The subtraction game

Alice and Bob play a game that starts by Bob picking a secret integer $N\ge100$. Then the game goes through several rounds. In every round, Alice picks an integer $x\ge3$. Every number can be picked ...
33
votes
9answers
4k views

Thirty genuine and seventy fake coins

In the country Curgonia, there are many types of fake coins and only a single type of genuine coins. The weights of these coins satisfy the following conditions: All genuine coins have the same ...
25
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3answers
1k views

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 ...
25
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3answers
1k views

Welcome to Oɴᴇderland

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...
21
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6answers
7k views

3x3 “Magic Square” of Prime Numbers

During the thinking and analysis of some mathematical problems, I came up with this puzzle: Just like any magic square, one has to fill in $9$ different numbers $P_1, P_2, \dots P_9$ to a $3 \times 3$...
-1
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14answers
2k views

Move one thing in the equation [closed]

$1484 / (7 / 9) = 19$ Make the equation true by moving one continuous shape or operation in the equation.
35
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3answers
3k views

The Determinant Sudoku

The determinants of $2\times 2$ matrices are calculated this way: $$\det\begin{bmatrix}a & b \\c & d \end{bmatrix}=ad-bc$$ And here's the sudoku-determinant puzzle: What's the solution for ...
35
votes
2answers
872 views

lolcatz can haz ur infinit cheeseboard

This is a problem on an infinite chessboard with pieces called lolcatz. They can move like queens or knightriders, but have a strange disadvantage... ... you've never heard of knightriders? Well, ...
33
votes
7answers
6k views

Living next door to Alice

Bob and Charlie live in a small village with 99 houses, numbered from 1 to 99. One day they meet Alice, a person who has recently moved to this village. Bob asks her if her house number is a square ...
33
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3answers
5k views

First digit of 3^2020

Inspired by The last digit for 3^(2019) Can you find the first digit of $3^{2020}$ without a computer?
32
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8answers
6k views

Will the ant reach the car?

A car starts distance 1 from a wall then drives away at constant speed $ c $. There is a length of elastic tied between the wall and the car. Remarkably this doesn't affect the motion of the car (in ...
26
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2answers
2k views

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 ...
26
votes
4answers
2k views

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, ...
25
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3answers
3k views

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 ...
23
votes
3answers
2k views

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 ...
13
votes
5answers
3k views

What is the smallest positive integer, which can not be written without repetitions of digits and using arithmetics only?

Suppose you are allowed to use all 10 digits (0,1,2,...9) at most once each; 4 arithmetic operations ($-$,$+$,$\times$,$\div$), each any number of times; parenthesises to group operations; and you can ...
12
votes
3answers
1k views

Which Flight Takes Me Home?

My vacation just ended, and I'm at the airport headed back home! It was definitely an enjoyable trip, but it could also be described as, well, unusual. I've got a more immediate problem though. I've ...
45
votes
4answers
6k views

x⌊x⌊x⌊x⌋⌋⌋ = 2020

Solve for $x$: $$ x \left\lfloor x \left\lfloor x \left\lfloor x \right\rfloor \right\rfloor \right\rfloor = 2020. $$ The floor function $\left\lfloor t \right\rfloor$ has the usual “greatest integer ...
39
votes
22answers
8k views

Aproximating 100 by 6

You're a fan of pen & paper RPGs and have finally arranged a new playing group, recruited amongst your friends from the mathematical faculty. As a GameMaster (GM) you've assumed that all your ...
32
votes
4answers
2k views

The Devil's Brother

The 1933 movie "The Devil's Brother" (also known under the title "Fra Diavolo") takes place in the Northern Italy of the early 18th century. Stan Laurel and Oliver Hardy play the fierce robbers ...
31
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9answers
9k views

Should I Take the Bus or Refill My Bottle First?

This is a real-life puzzle encountered by one of my friends. I want to arrive early to my class today. Exactly every $7$ minutes, there is a bus that arrives at the station near my dorm and will ...
26
votes
3answers
5k views

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 $28x+30y+31z=3650$?
25
votes
1answer
807 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 ...
24
votes
3answers
1k views

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 ...
20
votes
12answers
9k views

What's the largest number you can spell?

If I give you one of each letter in the alphabet what's the largest you can spell (in word form)? Bonus: What's the smallest? Bonus 2: What if you can use the words "minus", "plus" and "times"?
20
votes
7answers
3k views

Ali Baba and the 10 thieves

EDIT: This puzzle originates from the "International Mathematics Tournament of the Towns", and was published in the book "S.M.A.R.T circle overview" by Professor Andy Liu. The author has (albeit a ...
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 ...
16
votes
4answers
945 views

A Strange Planet with Strange Genders

You're a cosmonaut dedicated to exploring and understanding strange new worlds. The latest world you've arrived on has a species with three distinct genders which you've named Alpha, Beta, and Gamma. ...
16
votes
5answers
804 views

Maximize the number of paths

You have exactly 990 edges. Assemble them into a simple undirected graph with two distinguished vertices A and B, such that the number of different simple paths from A to B is as large as you can make ...
16
votes
2answers
1k views

Automatically a Knight, Knave, and Joker

Let M be a finite positive integer. It's exact value is not known. Suppose we have three classes of automaton, all of which accept a bit stream as input, produce a bit stream as output (one bit per ...
13
votes
1answer
558 views

Find the next number in this sequence

Find the next number in the sequence : 1; 5; 33; 25; 2; 16; 14; 12; 11; ? What is the next number and why ?
13
votes
2answers
894 views

The impossible digital sum

There are 10 digit numbers you are supposed to use shown as below; And there is a very special addition where every digit is used only once. As you see, most of the digital signals (blue squares) are ...
7
votes
4answers
944 views

Nerd on the Loose I - WHEN

Chat. I've created a chat room in case anyone wish to discuss this further. Preface. This is the first time I'm creating a puzzle. Since I find enjoyment in science and technology, the series of ...
1
vote
2answers
150 views

Move something in the equation

$1484 / (7 / 9) = 19$ Make the equation true by moving one continuous shape or operation in the equation. (You are NOT allowed to make an inequality or equality sign or touch the = sign.) You can‘t ...
31
votes
1answer
3k views

Ernie and the Island of Stability

Unfortunately, it appears that I may have misled you a little in this puzzle (as you probably know - my memory of events isn't always perfect). When I was writing it, I re-checked the Kzijekistanian ...
30
votes
2answers
3k views

Ernie and the Alchemist's Gift

For Ernie, the task of choosing Christmas presents for his friends is always a struggle. I think that is because, while he finds it easy to solve problems relating to machines, mathematics, and ...
29
votes
13answers
14k views

10 9 8 7 6 5 4 3 2 1 = 2016

Add the four basic operators $\times\div+\,\;-$ and optionally brackets to: $10 \quad 9 \quad 8 \quad 7 \quad 6 \quad 5 \quad 4 \quad 3 \quad 2 \quad 1$ To get the total $2016$. Rules: We are ...
28
votes
1answer
3k views

The largest Monday number

A Monday number is a positive integer $N$ with the following three properties: The decimal representation of $N$ does not contain the digit 0 The decimal representation of $N$ does not contain any ...

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