# 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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### Alternating between columns and rows after the shape becomes roughly square [closed]

Suppose I have $p \times q$ be any grid where $p \leq q.$ For example: My task is to alternate between columns and rows of the grid after the shape becomes roughly square and find it's cost. I asked ...
• 27
1 vote
91 views

• 165
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### What day of the week I am?

I am the day of the week that wants to be the first day of a year that is a perfect power. I do not like odd years. In order to be a perfect power, the year must end one day of the week later than the ...
485 views

### Productive Squares

Consider a productive square of size $n$ to be an $n\times n$ grid filled with a permutation of the integers in $[1, n^2]$, such that the product of all the numbers along the first row is equal to ...
• 2,232
169 views

### Maths olympiad of class 10 [closed]

How many 6digit numbers of the form XYZZYX (where Y is prime) are possible which are divisible by 7 A 42 B 56 C 70 D 84
147 views

### Seven birds in search of food [closed]

Seven birds live in a nest. They are very organized; each day three of the birds fly out in search of food. In n consecutive days, every pair of birds has been in exactly one of the n daily search ...
188 views

### Strings of Kind Numbers

A positive integer is said to be “kind" if it is divisible by one of its digits other than 1 (https://oeis.org/A185186). A kind string of numbers is a finite sequence of numbers all of whose ...
335 views

### Making an expression with the numbers 1 to 100 odd (or even)

Anna and Boris play a game with the numbers from 1 to 100 written in order in a row. Anna goes first, and turns alternate thereafter. In each move, a player puts one of the operation signs +, − and × ...
• 7,624
979 views

### Walking in a random direction

I walk $\pi$ km in one direction followed by $\pi$ km in another direction. In expectation how far am I now from my starting location? Both directions are chosen uniformly at random between $0^{\circ}$...
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368 views

### Rooks covering Dark Squares on a Chessboard

How many rooks are required such that all dark squares on the chessboard are covered by at least one rook.
• 2,232
1 vote
58 views

### Change all eight numbers to 1 [duplicate]

A solitaire game starts with eight numbers arranged in a circle. Each is either 1 or −1, and the choice is arbitrary. In each move, one can multiply any three adjacent numbers by −1. Prove that one ...
• 7,624
86 views

### Insert operators into 3 5 7 = 7 [closed]

How can you insert any math symbol/operation () ! - + x / square root etc into 3 5 7 = 7 without adding any numbers or changing the order? For example, 3-7+5=1 or 3+7-5=5. Also, try to solve 3 7 5 = 2,...
• 27
421 views

### The Kyiv Triangle Game

There are a number of triangles of various sizes in the figure below whose three vertices are among the vertices and edges on display. Two players, Alice and Bob, take turns coloring with their own ...
199 views

### Convolution (Literally)

Decode the following message. Hint: Additional hint:
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355 views

### A three star number puzzle

My mother's math department struggled to solve this problem; apparently only one teacher did. I was surprised as I thought it was trivial. Source: my mother's telegram message
• 43
346 views

### Proving that a particular order is impossible

A friend shared this puzzle with me on Discord: There are 5 bowls, labelled 1, 2, 3, 4 and 5. The bowls can only be moved around in pairs without changing the order of the pair. The bowls can also be ...
3k views

### Math is Awesome

I have a shirt. It says that $AWE+SOME=MATH.$ A, W, E, S, O, T, M, and H are not necessarily distinct positive integers from $0$ to $9$. The goal is to find the maximum possible value of $MATH.$ If ...
• 457
3k views

### Prove there's a day of the week for each number in a year

Prove, or disprove, that each day of the week (Monday to Sunday), falls on every date number 1 to 30 in the space of a year. I.e. Prove there is a Monday 1st, Tuesday 1st, ..., Sunday 1st in the time ...
• 57.6k
122 views

### Picasso at the art school [closed]

Picasso is preparing for his fine art exam. At the exam he will be shown exactly (a replica of) one of the following four paintings chosen uniformly at random: Mona Lisa The Last Supper The Starry ...
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### 1+3 Towers of Hanoi

There are four pegs in a row; let's call them A, B, C, and D from left to right. Peg A has a stack of $n$ differently sized disks, sorted in size so the smallest disk is at the top. All other pegs are ...
• 12k
146 views

### Unique day of the year

I made this challenge. Astronomers announced that the sky and the moon will appear violet-velvet next week, and one of their workmates is also celebrating her birthday on the day that the moon will ...
129 views

### Relation Between The Year And The Day

Today is January 22, the 22nd day of the year 2024. I chose today because 22 is my favorite number. Now for the problem. Try to relate 22 to 2024 using math. For example, 58 is related to 271 because ...
• 457
636 views

### Letters and Numbers

Every letter is a different value from 1-26 A x A = L + G C x C = U J x H = P + R W - K = N G + L = E + Z S + J = P - Y E x C = Z x B D + U = Z + E G x F = D + U O + X = V S x K = Z + E K x R = M D + ...
• 143
5k views

### Make 27 using 1, 1, 1, 1

Make the number 27 using 4 instances of the digit 1. You must use all 4 digits to make it count. Here are the allowed operators: Addition (+), subtraction (-), multiplication (*), division (/) Square ...
583 views

Which symbol is missing? Explain your reasoning.
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193 views

### Tatiana thinks of two numbers

My student Tatiana thinks of two positive integers, not necessarily different, none greater than 1000. I wish to determine her numbers, and for this she allows me any number of questions to which she ...
508 views

### Seven genuine and two fake coins

Seven genuine coins have the same weight. Two counterfeit coins also have the same weight. A counterfeit coin is heavier than a genuine coin. Identify the fake coins using a standard balance at most ...
• 7,624
1 vote
60 views

### calculating rotating partners, 2 teams of 3 people for 5 rounds [closed]

I want to make player sheets for 6 players (grouped into two teams of three players) on a rotating basis for 5 rounds. It seems that 5 people will play the same player 3 times, 2 times and one time ...
• 11
437 views

### Make expressions equal to 6 using exactly four 4s

You must use all four 4s. You may use addition (+). You may use subtraction (-). You may use multiplication, such as with asterisks (*) and/or grouping symbols. You may not use any division. You ...
• 1,576
231 views

### Henry Ernest Dudeney puzzle

An officer explained that the force to which he belonged originally consisted of 1000 men, but that it lost heavily in an engagement, and the survivors surrendered and were marched down to a ...
906 views

### What is the earliest 2024 can appear in an S-sequence?

A Sloane Sequence (or S-sequence) is any sequence of different positive integers begining with 1 in which the nth term (after the first) is the previous term plus n, times n, minus n, or divided by n ...
1k views

### Six-sevenths of a million this sum I’ll maintain. How is this possible?

To a thousand add one, twice fifty and ten, Six-sevenths of a million this sum I’ll maintain. The above puzzle appeared in the book, “Rational amusement for winter evenings” (1821) by John Jackson.
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250 views

### Constructing 2024 from the first 7 natural numbers

Can you use each number 1, 2, 3, 4, 5, 6, 7 exactly once, the four operations +, -, *, / and the parentheses to construct the number 2024? Bonus: can you find multiple distinct solutions? No computers ...
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