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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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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Tiling a dodecahedron
The surface of a dodecahedron is tiled with 6 of the shown tiles, each tile covering two faces of the dodecahedron. In how many essentially different ways this can be done?
Two tiled dodecahedrons are ...
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Ship collisions
Four ships are sailing on a 2D planet. Each ships traverses a straight line at constant speed. No two ships are traveling parallel to each other. Their journeys started at some time in the distant ...
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Colliding bullets [duplicate]
Every second, a gun shoots a bullet in the same direction at a random constant speed between 0 and 1.
The speeds of the bullets are independent uniform random variables. Each bullet keeps the exact ...
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Elapsed International Power
Clues: [contextual images] [beefcake horse] [beefcake horse reversed with 261] [x10]
Instructions: Name That Movie
_ _ _ _ T _ _ _ _ _ _ T _ _ _
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Tħε Wεαk αlpħα - Enigmatic Puzzle
Clues: [character image]
[In text bubble: #1/2, #2, #4]
[all raised to the -1 power]
Instructions: Name That Number
_ _ _ _ _ _ _ _ _ T _ _ _ _ _ _ _ _ _ _ _
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Counting Tic-Tac-Toe draws on larger grids
Alice and Bob play a game of Tic-Tac-Toe on a grid of size $N \times M$. The rules of this game are the same as the original Tic-Tac-Toe:
Alice plays first (white); Bob plays second (black).
On each ...
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Wounded Soldiers/Crossing a Bridge Puzzle - checking a solution
I am working on a Prolog university assignment, where we have to determine what the shortest time is for 4 wounded soldiers to cross a bridge to safety. This seems to be a variation of the more common ...
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Why whenever I repeat an algorithm on Rubik's cube 3 times the orientation of all corners remains the same?
I don't get why whenever I repeat an algorithm 3 times the orientation of all the corners magically returns back to normal. Here is where my confusion comes.
Let's say that some algorithm rotates the ...
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Find the value of $\bigstar$: Puzzle 12 - Not enough variables
This puzzle replaces all numbers (and operations) with other symbols.
Your job, as the title suggests, is to find what value fits in the place of $\bigstar$. To get the basic idea, I recommend you ...
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Capture a laser beam
Design a mirror box that can capture a laser beam, so that it will keep reflecting forever.
The setup looks like in the following image:
The goal is to design a box in a way, that the light beam will ...
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A dog, its owner, and the other person
2 people, A and B, are 300 meters away from each other and are walking towards each other in a straight line at 1 meter per second. A has a dog that can run at 2 meter per second. The dog runs in a ...
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If A cents can be paid with B coins then prove that B dollars can be paid with A coins
Looking for an intuitive solution to the following problem:
In a certain country the following coins are in circulation: 1 cent, 2 cents, 5 cents, 10 cents, 20 cents, 50 cents, and 1 dollar. It is ...
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Prime Twelve Apostles
You are given an empty square grid. Each cell can be an island with a positive integer $n$ or a bridge connecting islands. The following rules apply:
Each island with a number $n$ must have exactly $...
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The Twelve Apostles
You are given an empty square grid. Each cell can be an island with a positive integer $n$ or a bridge connecting islands. The following rules apply:
Each island with a number $n$ must have exactly $...
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Am but not equal
I am myself, but I am not equal to myself. What am I?
Hint:
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Sixteen Two's to get Two Thousand and Twenty-Two
Get the number 2022 by only using the number 2 a maximum of 16 times. There is a solution.
Allowed:
$+$
$-$
$*$
"$()$"
"$\frac x y$"
$x^y$ Note: When you use $2^2$, it counts as ...
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Expected power consumed
Suppose you have an 8x8 grid of electric bulbs. So you have 8 rows and 8 columns.
Now you can either switch on and supply power to entire row(or column), or switch it off and supply no power at all. A ...
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In the NYT Connections game, is there a guaranteed strategy to get the last two groups without knowing the theme?
Recap of the rules
You're given a grid of 16 words that have to be split into 4 sets of 4, each with a defining theme. For example, in today's puzzle, four of the words are 'iguana', 'monitor', 'gecko'...
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Fewest polyominoes adjacent to 3 copies
What is the smallest positive number of polyominoes P, such that
You can place grid aligned copies of P without any overlap; and
Each polyomino is adjacent to exactly 3 other polyominoes.
...
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How is the tree colored?
Not relevant fiction context
Paul's journey in the mathematical forest began this early morning. You know, he is a Biomathologist!
He saw a lot of spectacular plants, geometrical flowers and fractal
...
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Smallest polyomino adjacent to 3 copies
What is the smallest polyomino P in number of cells, such that
You can place grid aligned copies of P without any overlap; and
Each polyomino is adjacent to exactly 3 other polyominoes.
Polyominoes ...
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Help a woman from ancient Rome find out how her husband is doing
Let's go back 2000 years. A woman named Valeria received a strange message from her husband Claudius who is a frumentarius.
The message:
...
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If ABCDE*4 = EDCBA. A,B,C,D and E are all natural numbers ( 1-9) without repeating any natural number. Why is it deducible that E cannot be three?
If ABCDE*4 = EDCBA. ABCDE,EDCBA are five digit numbers. A,B,C,D and E are all natural numbers ( 1-9) without repeating any natural number. Why is it deducible that E cannot be three?
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Fill a 4x4 grid with minimal sum of positive integers in a way that adjacent cells contain numbers of different parity
Find a 4x4 grid containing 16 unique positive integers with minimum sum, such that adjacent numbers have different parity.
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Which positive integers have at least one positive integer multiple such that the base 10 representation of that multiple has only even digits?
Which positive integers N have the property that there exists at least one positive integer multiple of N such that the base 10 representation of that multiple has only even digits?
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How abundant can a number get?
Famously, a perfect number is equal to the sum of its proper divisors. For example, 28 is equal to 1 + 2 + 4 + 7 + 14. If the sum is more than the original, the number is called abundant, and if the ...
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Finding the larger number with a minimal number of questions
Bob and Charlie each secretly chose a 300 decimal-digit number, possibly with leading zeroes. We want to find the value of the larger number. We may address each question to either Bob or Charlie, and ...
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An immortal ant on a gridded, beveled cube divided into 3458 regions
This puzzle takes place on the surface of the following gridded, beveled cube:
The surface of this cube is divided into 3458 small regions separated by black lines. Of these regions, 3450 of them are ...
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The shorter the message, the larger the prize (version II)
This is a successor question to The shorter the message, the larger the prize . For completeness I will include the entire question even though only the numbers have changed. Solutions to this puzzle ...
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A magic grasshopper
A magic grasshopper sits at the origin of a number line. He can jump a distance of 1, 2, 4, 8, ... or any whole power of 2 in either direction. What is the smallest distance from the origin that ...
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Calculate a fictional animal based on real animals
Given the following equations:
With the following data:
Could you find the answer?
Note: the icons resemble the animals, you don't have to look at (for example) the colors how the icons are painted,...
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An Infinitude of Perfidious Pupils
Here's an original puzzle I created. Enjoy!
A teacher had infinitely many students, and he referred to them by the designations $\text{Student } 0$, $\text{Student } 1$, $\text{Student } 2$, and so on....
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