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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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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 ...
30
votes
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 ...
25
votes
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 ...
25
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 $28x+30y+31z=3650$?
24
votes
1answer
788 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 ...
23
votes
3answers
990 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 ...
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 ...
16
votes
5answers
775 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 ...
15
votes
4answers
931 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. ...
13
votes
1answer
522 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
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 ...
13
votes
2answers
808 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
939 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 ...
24
votes
8answers
5k views

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 ...
21
votes
3answers
796 views

Master Bomb Defusers

Day 115 of your investigation and you and your ever-faithful-if-only-a-bit-slow partner have finally caught the trail of your arch-nemesis, a serial bomber known only as "Mr. 5". Doing your best to ...
21
votes
4answers
6k views

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 ...
19
votes
17answers
9k views

Number 88 from the digits 2, 0, 1 and 7?

Can you use the digits 2, 0, 1 and 7 each only once to create the number 88?
17
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6answers
5k views

What is the expected value of this coin flipping game?

A casino offers the following game: You flip a fair coin repeatedly and record the results on slips of paper, one result per slip. At any time you may decide to stop, at which time one of the slips ...
15
votes
1answer
1k views

Touching matchsticks with compass and straightedge

The question Touching Matchsticks asked for the smallest matchstick graph where every node is connected to four distinct edges. The Harborth Graph is the smallest such, with 104 edges connecting 52 ...
14
votes
7answers
2k views

Twelve balls on a scale, where one ball is lighter and another is heavier

Suppose you have twelve identical-looking balls. Ten of them are the same weight, but one is slightly lighter and one slightly heavier, in such a way that the weight of the lighter and heavier ball ...
13
votes
5answers
1k views

A row of 2015 red and white chips

There is a row of 2015 chips, of which 2014 are white and one is red. You are allowed to make moves of the following type: "Choose one red chip, and flip the colors of its two neighboring chips (from ...
13
votes
3answers
637 views

Exponential time in a Blue Eyes variant

I created a variant of the Blue Eyes problem where the logic took 4901 days (over 13 years) to totally play out. I thought this was nice, but I was hoping for an even longer period of time. Of ...
11
votes
2answers
632 views

A crawling spider and a cautious fly

Inside a rectangular room, measuring 16 feet in length and 8 feet in width and height, a spider resides at a corner. A fly buzzing in the room intends to land at a spot that will take the spider the ...
10
votes
4answers
955 views

Cutting a square into seven rectangles

Cosmo has cut a square into seven rectangles, so that the seven lengths $\ell_1,\ldots,\ell_7$ and the seven widths $w_1,\ldots,w_7$ of these rectangles satisfy $$ \{\ell_1,\ldots,\ell_7\}\cup\{w_1,\...
10
votes
2answers
2k views

What is the next number in this sequence? 0, 1, 11.2, 10.2, 113.2, 103, 103.2, 0.2, 1.2, 2.2, 2, …

0, 1, 11.2, 10.2, 113.2, 103, 103.2, 0.2, 1.2, 2.2, 2, ? The only hint I'll give at this stage is that the sequence is infinite. If nobody gets it within a few days, I'll give a few terms that come ...
9
votes
3answers
2k views

Sum, Product and Difference

I had three mathematician friends at school, and we were hanging out. Out of the blue a question came to my mind, and I decided to ask it to them: "Guys, I have a question for you. Which is actually ...
9
votes
7answers
49k views

Make numbers 1 - 32 using the digits 2, 0, 1, 7

This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 7. Rules: Use all four digits exactly once Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, square root ...
7
votes
2answers
633 views

2016 coins and a balance

On the table, there is a balance with two pans. The display on the balance tells the difference between the weight in the left ban and the weight in the right pan (measured in gram). There are also $...
30
votes
1answer
2k views

Computation without a computer

In the number $(1+\sqrt{3})^{2015}$, what is the 224th digit after the decimal point? You may NOT use a calculator, computer, or any electronic aid to answer this question. Only pen(cil), paper, and ...
28
votes
3answers
4k views

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 $...
25
votes
4answers
1k views

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, ...
25
votes
2answers
4k views

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 ...
24
votes
10answers
3k views

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 ...
19
votes
3answers
2k views

An arithmetic puzzle from 1645

The following problem is found in the first Norwegian arithmetic, published in 1645 by Tyge Hansøn: Three hundred oxen large and small, A cattle owner wanted to buy: 3 for 63 daler he got. ...
16
votes
5answers
2k views

Should the angels play their game?

Two angels in heaven want to play a game. One of them comes up with an arbitrary, computable function from the integers to the integers. The other angel has to guess what it is. The second angel can ...
15
votes
5answers
2k views

Important days in history… and to come!

The other day I decided I wanted to come up with another simple puzzle before releasing another toughy on puzzling.SE. I came across an interesting series of dates that I wanted to share and see if ...
14
votes
6answers
1k views

Finding Doctor No

James Bond is invited to a party with altogether $128$ participants (including Bond himself, the host, and the hostess). At the beginning of the party the host takes James Bond aside and asks him to ...
14
votes
2answers
723 views

How many ways to pick the fruit

Alice and Bob have a farm in the form of a $20 \times 20$ grid, each square in the grid containing the same amount of fruit. They both live in the lower-right square. Luckily for them, Alice is a ...
13
votes
3answers
1k views

Black and White

OK guys, I think this is my best puzzle yet. Hope you enjoy it, the solution is neat and simple. A boy draws 2015 unit squares on a piece of paper, all oriented the same way. The squares can ...
13
votes
7answers
3k views

Fair n-sided dice

I have recently bought a fair $10$-sided dice for generating equally distributed random numbers from the range $1,2,\ldots,10$. Let me describe this dice in some more detail. Consider a regular 5-gon $...
12
votes
4answers
825 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. ...
12
votes
6answers
4k views

Find two numbers based on either their product or their sum?

A friend of mine told me the following puzzle and I could not solve it. Sam chooses a positive integer $x$, and Peter chooses another number $y$. They do this secretly, so that Peter does not know ...
11
votes
11answers
10k views

Make 6 5 4 3 = 81

Can you find a way to make: 6 5 4 3 = 81 by concatenation and/or adding any of (and only) these mathematical operators: + - × ! ÷ ^ standard parentheses () You cannot add other numbers to the ...