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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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 ...
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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 ...
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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?
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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!
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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.)
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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 the number ...
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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, _, _, _, _, _, _, _, _, _, _, ...
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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 ...
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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 ...
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#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 = ...
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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.
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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. ...
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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.
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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 ...
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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.
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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,...
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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 ...
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Decipher a long sequence of numbers
51699624576811268526783109824167925197245652924177251787241782538786302873119768312852668312686625268245686752824473216878253830287925175273039778250852831287672527245665263006725397251762529312811498
...
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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 ...
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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.
...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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.
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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 ...
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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^{...
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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 ...
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Villeta's Soup of Primes
i) Hidden in this 8 x 8 board are the first 31 primes starting with 2 and up to to 127. They occupy adjacent, non-overlapping cells (up to 3), and are read horizontally (from left to right) or ...
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