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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18 votes
1 answer
1k views

It's what's within the two

What is the answer to this puzzle?
Prim3numbah's user avatar
  • 27.4k
4 votes
4 answers
1k views

Numbers that are averages of their digits

A number is called special if its decimal value^ is the average of its digits. How many special numbers are there? Bonus: How many special numbers do not begin with the digit 0? Good luck! ^ You are ...
Dmitry Kamenetsky's user avatar
18 votes
1 answer
2k views

Reducing π to zero (again)

You are given the first 20 digits of π: 31415926535897932384. In each move, you can select a contiguous group of 5 digits and increase/decrease them all by the same integer, provided that each ...
Will Octagon Gibson's user avatar
11 votes
8 answers
2k views

frog on a number line

A Frog is at C. The purple numbers are the probability that the frog jumps in that direction when it is at certain place. The frog stops at A or E. What is the probability that the frog stops at A? ...
TheHappyBee's user avatar
16 votes
3 answers
2k views

Interesting irrational number

Can you find an irrational number $x$ such that $x$, $1/x$ and $x^2$ all have exactly the same digits after the decimal point? Good luck!
Dmitry Kamenetsky's user avatar
1 vote
2 answers
204 views

Logic and Geometry Problem #5: does Savage Go have cycles?

My question is whether or not a cycle can occur in the game of Savage Go. That is, you kill some of mine, I kill some of yours, you kill some of mine... Endless cycle of turns. Game never finishes. No ...
Mark Steere's user avatar
1 vote
1 answer
196 views

How many 4x4 Latin Squares are there?

I thought of this problem when playing Sudoku. Let A = {1,2,3,4}. I have to make a 4x4 box (i.e. the size of A in both dimensions) and fill it with data such that ...
HelptimeCode's user avatar
4 votes
1 answer
684 views

Don't let 'em die!

There is an 8x8 array of sleeping humans with ten feet between adjacent humans, with sides in the four cardinal directions. A hero and a villain start ten feet west of the northwest human. The hero ...
mathlander's user avatar
4 votes
2 answers
271 views

Waffleing my Egg

This morning I had a waffle and a fried egg for breakfast. The fried egg was cooked with a mold, so it was perfectly round and three inches in diameter. The waffle was a 3-inch by 4-inch grid of one ...
DqwertyC's user avatar
  • 7,909
21 votes
2 answers
2k views

Can you find a 3x3 white square somewhere in this relatively prime graph?

This puzzle comes from: http://skepticsplay.blogspot.com/search/label/puzzles Wow, it's been some time since I've posted a puzzle! Here's a simple pure math puzzle off the top of my head. Back in ...
Will Octagon Gibson's user avatar
5 votes
1 answer
310 views

Permutations with given longest increasing subsequence

How many permutations of 1 to 20 are there with 2,5,6,9,13 as a longest increasing subsequence? (It may be tied with others.)
Simd's user avatar
  • 6,627
7 votes
5 answers
548 views

Minimum K for detecting fake pearls in one weighing

There are 10 boxes, each with the same number of pearls (represented by K). Genuine pearls weigh 30g each, while fake pearls weigh 29g each. Each box is either all genuine or all fake, and any number ...
Pumbaa's user avatar
  • 814
1 vote
0 answers
78 views

Can you find the missing letters?

A pattern of letters has had letters 10 through 20 deleted. Your job is to find out what letters should go in spots 10-20. Here is the pattern: a, b, c, d, d, d, f, e, f, _, _, _, _, _, _, _, _, _, _, ...
BigMistake's user avatar
2 votes
4 answers
323 views

Cutting the points evenly

I draw an even number of points on a piece of paper. Is it possible to cut the paper into two pieces with a single straight cut, such that: Each piece gets the same number of points The cut does not ...
Dmitry Kamenetsky's user avatar
5 votes
1 answer
183 views

Puzzling Pelican Pebbles

Story Setup It's Percy the Pelican's first day running the front desk of his master's magical pebble shop. His job is to fetch pebbles from the stock room to fulfill customer orders. The stock room ...
DqwertyC's user avatar
  • 7,909
1 vote
1 answer
225 views

#TenderfootSpiral

Clues: Two hikers on an incline arrow with numbers. Hiker 1 says: 38.548493. Hiker 2 says: -105.998749. Sequence: Hiker 17711 Hiker 0 377 0 144 1 10946 233 987 0 2584 6765 75025 Hiker = ...
Tyler's user avatar
  • 999
6 votes
1 answer
223 views

Intermingled primes

This puzzle is part of the Monthly Topic Challenge #14: Think inside the (very small) box!. 6 different, 3 digit primes are stacked here in two layers. You only see the sum of overlapping digits. ...
Retudin's user avatar
  • 7,654
2 votes
0 answers
89 views

Another paint balls problem [closed]

Suppose you have 2n balls with 1 of them being red and the rest being white. In each round the balls are randomly paired into n pairs. All white balls in a red-white pair are painted red. What is the ...
Yuxiao Liu's user avatar
7 votes
1 answer
380 views

Closed path on a dodecahedron

Your task is to draw lines between edges on a regular pentagon such that if you tile a dodecahedron with 12 identical copies of that pentagon you get a single closed line which does not intersect ...
Herbert Kociemba's user avatar
0 votes
2 answers
197 views

Expected number of steps [closed]

There are N cars that are parked in N parking spots numbered from 1 to N. After the Nth parking spot, there are N more parking spots numbered from N+1 to 2N. At each step, a car is selected randomly ...
12HackingEarth's user avatar
0 votes
1 answer
135 views

The Triangular Cannonball Problem [closed]

How many ways are there to stack an equilateral triangle of cannonballs into a tetrahedron of cannonballs? In other words, how many positive integers are both triangular and tetrahedral?
gyancey's user avatar
  • 519
45 votes
4 answers
2k views

A colorful dodecahedron

Divide a "base" edge of a regular pentagon into three equal parts. Then draw two lines from the base to the center of the other edges such that the lines do not intersect. This splits the ...
Herbert Kociemba's user avatar
126 votes
5 answers
140k views

Is this duplo train track under too much tension?

My kids were making this train track of duplo the other day, and this is what they put together. They are still very young, and for them, this is something big. They were really proud that they ...
Lezzup's user avatar
  • 4,834
-1 votes
1 answer
207 views

Figure Out The Language: Min

Imagine there is a programming language in which you can only evaluate expressions. Expressions have operators and constants. There are three types of constants. Numbers - Any number from 0 to ...
The_AH's user avatar
  • 105
5 votes
0 answers
122 views

Connect dots on a grid with one continuous line (optimization)

(This question is the third puzzle of the Connect dots puzzle series. You can find the first two puzzles here and here, respectively. The original question and photos originate from webadventurer. ...
CatProgrammer's user avatar
4 votes
1 answer
188 views

Find unique values for the variables to make all statements true

In this puzzle you have to find unique values for the variables to make all statements true. I have proceeded to here and now I seem to be stuck.
Teodor Dyakov's user avatar
3 votes
3 answers
301 views

Logic and geometry problem #4: are these games functionality equivalent?

Two games, Crossway and Mincut, are believed to be functionally equivalent. That is, a win by Crossway rules will necessarily lead to a win by Mincut rules. And a win in Mincut will be a win in ...
Mark Steere's user avatar
1 vote
1 answer
129 views

Regular polygons meeting at a point

How many ways can regular (convex) polygons meet at a point (vertex), so there are no gaps or overlaps? Here's an example with a square, hexagon, and dodecagon.
qwr's user avatar
  • 693
2 votes
1 answer
120 views

Tile 1x2 dominoes in a 2x10 space

How many ways are there to tile unmarked 1x2 dominoes in a 2x10 space? Bonus: What if the dominoes were identical and had pips on their front (face-up), so they could be distinguished by 180 degree ...
qwr's user avatar
  • 693
-4 votes
1 answer
161 views

Find the Rat in the Hole

A rat is in one of 100 holes that are in a line. Each night he moves to the left or right 0,1, or 2 holes randomly selected. You pick one hole each day to look in until you find him. What procedure ...
Bob Bixler's user avatar
17 votes
1 answer
750 views

Poetry of the stars

Prof. Levenshtein is meant to be teaching us astronomy, but they fancy themselves as a poet. Can you figure out the name they've given to each star?
andypea's user avatar
  • 273
3 votes
3 answers
778 views

Was Humpty Dumpty right?

Raymond Smullyan's What is the Name of This Book? contains a puzzle which I'll paraphrase here: Of the identical twins Tweedledum and Tweedledee, one of them lies on Mondays, Tuesdays and Wednesdays ...
fblundun's user avatar
  • 932
5 votes
2 answers
700 views

Number of 1's needed to write all primes up to P

i) Find, if it exists, a prime P such that the number of 1's used to write all the primes from 2 to P is precisely P. ii) Are there infinitely many such P? If not, find them all. These questions ...
Bernardo Recamán Santos's user avatar
16 votes
1 answer
534 views

Game of the glasses on the windowsill

The windowsill above the sink is where my wife and I place our dirty wine glasses. And while both of us love each other, neither of us love loading the dishwasher. As a result, these dirty glasses ...
Feryll's user avatar
  • 2,222
8 votes
1 answer
313 views

Alice knows a+b, Bob knows a×b. Can we find (a,b)?

There are two distinct positive integers $a,b$ (i.e. $a\neq b$) such that $a < 7$ and $b < 7$. Alice has been told the sum of $a$ and $b$. Bob has been told the product of $a$ and $b$. Both ...
Hemant Agarwal's user avatar
7 votes
8 answers
2k views

9 trees in 7 rows with 3 trees in each row

The following puzzle is a variant of a puzzle published in the May 8, 1926 issue of THE WINNIPEG TRIBUNE MAGAZINE: In the picture below there are nine trees arranged in two rows with five trees in ...
Will Octagon Gibson's user avatar
13 votes
1 answer
605 views

Self-referential sequence that is sometimes powers of two

I've created an integer sequence where, after the first two elements, every element is calculated using the previous two. If the first two numbers are $1$ and $3$, the sequence goes as follows: $$1, 3,...
Peter's user avatar
  • 583
5 votes
1 answer
159 views

How to swap position of two elements when you can only rearrange four of them by one-way rotation?

The following puzzle is the final puzzle in the video game "Grim Tales: The Bride". Is there a methodical way of solving this type of puzzle? Can I plan steps to swap the position of the red ...
Felix's user avatar
  • 53
-5 votes
1 answer
195 views

Decipher a long sequence of numbers

51699624576811268526783109824167925197245652924177251787241782538786302873119768312852668312686625268245686752824473216878253830287925175273039778250852831287672527245665263006725397251762529312811498 ...
web adventurer's user avatar
4 votes
1 answer
317 views

Leonardo Da Vinci's Magic Calendar

It is the year 1468 and young Da Vinci has built a magic calendar going back to Jesus. Here's how it works: Given 7 distinct years between 33 and 1468 inclusive, the arranger discards one and orders ...
Display name's user avatar
  • 2,230
2 votes
1 answer
156 views

Logic and geometry problem #3: are cycles possible in Scattercut with added "maximum" rule?

My question is whether or not cycles can occur in the game of Scattercut. That is, you kill some of mine, I kill some of yours, you kill some of mine... Endless cycle of turns. Game never finishes. ...
Mark Steere's user avatar
12 votes
3 answers
761 views

What do 84, 96 and 108 have in common?

There's a certain property that's shared between (as far as I know) infinite positive integers including 84, 96 and 108. Below are the first thousand numbers with this property; I added that many in ...
Peter's user avatar
  • 583
0 votes
0 answers
73 views

Find the largest number with unique digits, that is divisible by each of its digits [duplicate]

Find the largest number with unique digits, that is divisible by each of its digits. For example 132 has unique digits and is divisible by 1, 2 and 3. But it is not the largest such number. Can you ...
Teodor Dyakov's user avatar
5 votes
1 answer
197 views

14 coins problem but you can't understand the scale

The 12 coins 12 coins problem but you can't understand the scale asks for is not the maximum possible, therefor this follow-up question: You have a number of coins, one is fake but you don't know ...
Retudin's user avatar
  • 7,654
6 votes
2 answers
216 views

How many solutions to the twelve coins problem are there?

I was recently asked to solve the classic twelve coins balance problem: You are given twelve coins, eleven of which are equal in weight and one of which is either heavier or lighter than the other ...
Kevin H's user avatar
  • 163
10 votes
2 answers
635 views

Pay each amount with at most two coins

Euro cent coins come in the denominations 1, 2, 5, 10, 20 and 50 cents. You are inconvenienced by the fact that you need a lot of coins to pay each amount up to 100 cents. To pay 99 cents, you need 6 ...
Tilman's user avatar
  • 103
31 votes
13 answers
6k views

2 vs. 1.005^200

Without using a calculator or a computer can you determine which of these two numbers is bigger: $2$ or $1.005^{200}$ ? I saw this puzzle in a YouTube video, which I will post later.
Dmitry Kamenetsky's user avatar
7 votes
3 answers
490 views

Colliding Bullets again

Here's a colliding bullets problem of my own devising that's different from previous versions. Every second a gun has a 60% chance of firing a bullet in a straight line. After 10 seconds there would ...
Bob Bixler's user avatar
1 vote
1 answer
113 views

Reversing a binary string with a restricted Turing Machine

Some malevolent entity (me) asks you to construct a Turing Machine which, given an input on its tape of the form $LbR$ where $b$ is some binary string, changes this to $Lb^{-1}R$ then halts (where $b^{...
volcanrb's user avatar
  • 121
13 votes
5 answers
3k views

Are there always 2 teams such that they have together defeated every other team

In a tournament without draws, every two of the nine teams play against each other exactly once. Must there always be two teams such that every other team has lost to either or both of them? From the ...
Hemant Agarwal's user avatar

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