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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7 votes
2 answers
343 views

The shady puzzle that will keep you in the dark

The image below is the horizontal cross section of a room. The bulb shows the position of the single light source. When the light is switched on, one wall (marked in brown) remains completely in ...
Will Octagon Gibson's user avatar
18 votes
1 answer
1k views

An Amazing Configuration

Ed Pegg found in December 2019 this amazing configuration consisting of 22 points in 28 lines of 4. On those points place 22 different positive integers such that the sum of any of the four points in ...
Bernardo Recamán Santos's user avatar
1 vote
0 answers
117 views

Maximum filled days

I have two types of items, $i_1$ and $i_2$. $i_1$ items can be used at most $50$ times and $i_2$ items can be used at most $120$ times. I have $7000$ items $i_1$ and $800$ items $i_2$. Each item $i\in ...
JKHA's user avatar
  • 6,005
-2 votes
1 answer
211 views

Circle Point Region Puzzle

Below puzzle was given to me by my friend. His college professor gave him to solve. Answer is one (real) word only. HINT: Turn around when one could be confused Here is the puzzle:
Curiospire's user avatar
18 votes
1 answer
1k views

Which heptomino is it obvious can't tile the plane?

A polyomino is a collection of equal-sized squares joined edge-to-edge in the plane (think Tetris pieces, but with an arbitrary number of squares instead of just four). A heptomino is a polyomino ...
Lieutenant Zipp's user avatar
12 votes
0 answers
195 views

The Snake and the Hunter

The Snake and the Hunter is a game for two players who play in two rounds interchanging the roles of snake and hunter. The game is played in a rectangular grid of points, say 6×6. In both rounds the ...
Bernardo Recamán Santos's user avatar
11 votes
4 answers
3k views

Why, crystal ball? Why?

I stare deep into my crystal ball, allowing it to reflect myself, to encompass everything of who I am. Through my reflection on its surface, I gaze into its misty, murky depths, hoping to catch a ...
isaacg's user avatar
  • 5,807
5 votes
2 answers
1k views

Football Pass Rate Paradox [closed]

There are 2 teams - Team A and Team B. Both teams play 2 matches. In both matches, Team A has a higher pass rate than Team B. Can the overall combined pass rate for Team B be higher than that of Team ...
quantrader23's user avatar
14 votes
7 answers
3k views

Join six cities with roads

Warmup question: Each of five cities is connected to the others by four roads. Show that it is possible for the roads to intersect only once with exactly two roads crossing over at that single ...
Will Octagon Gibson's user avatar
1 vote
0 answers
107 views

Seven thieves and diamond problem where the remainder increases with the number of thieves [duplicate]

Seven thieves steal a certain number of diamonds. On the way back home they all decide to take a nap under a tree. While the others are asleep, two of the thieves wake up and decide to divide the loot ...
Amber Michelle's user avatar
6 votes
2 answers
967 views

BROWN + YELLOW = PURPLE [closed]

This is a Cryptoarithmatic, where each letter denotes a single digit number. Find values of all the letters. BROWN + YELLOW = PURPLE Please show your method for solving this question.
Anuraj's user avatar
  • 69
6 votes
3 answers
1k views

3x3 grid with no isosceles triangles of the same colour

Can you paint the 16 nodes of a 3x3 grid in three colours, such that no three nodes of the same colour form the vertices of an isosceles triangle? Note that we allow isosceles triangles to have zero ...
Dmitry Kamenetsky's user avatar
7 votes
2 answers
411 views

6x6 grid with no three cells of one colour in a line

Can you paint the cells of a 6x6 grid in three colours, such that no three cells of the same colour lie on a straight line passing through their center?
Dmitry Kamenetsky's user avatar
1 vote
1 answer
94 views

4x4 grid with no three cells of one colour in a line

Can you paint the cells of a 4x4 grid in two colours such that no three cells of the same colour lie on a straight line passing through their center?
Dmitry Kamenetsky's user avatar
9 votes
1 answer
299 views

Designing a four-pan scale

You are an ancient merchant, and you need to weigh out many different items of many different weights. To do so, you'll design a scale to weigh objects. Unlike a standard scale, your scale will have ...
isaacg's user avatar
  • 5,807
3 votes
1 answer
205 views

How to make 2012 by using 2, 0, 1, 2?

How to make $2012$ by using $2, 0, 1, 2$? Allowed Operations: Addition, Subtraction, Multiplication, Division, $!$ (factorial), subfactorial ( $!n$), primorial (product of the first $n$ primes), ...
Thirdy Yabata's user avatar
5 votes
4 answers
685 views

How to get the numbers from 50 - 100 with the numbers 2, 0, 2, 4

All I need is 56-59, 69, 73, 75- 77, 79, 86, 90-94, 99. I've done the rest but I would love to hear other solutions. Rules: Use any of the following operations: basic operations (+ - x /), to the ...
bob's user avatar
  • 69
-4 votes
1 answer
81 views

Make numbers 1 - 30 using the digits 2, 0, 2, 5

Try to make all numbers 1-30 using the digits 2, 0, 2, 5. Rules: Use all four digits exactly once. Allowed operations: $+,−,×,÷,! \text{ (factorial)}, !! \text{ (double factorial)}, !!! \text{ (...
WOWOW's user avatar
  • 165
-3 votes
1 answer
210 views

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 ...
Thirdy Yabata's user avatar
7 votes
1 answer
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 ...
Sny Smartie's user avatar
  • 2,254
-2 votes
1 answer
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
Vanita Gawande's user avatar
0 votes
2 answers
152 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 ...
Pokemon15's user avatar
4 votes
2 answers
190 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 ...
Bernardo Recamán Santos's user avatar
4 votes
2 answers
337 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 × ...
Will Octagon Gibson's user avatar
8 votes
3 answers
984 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 $0^{\circ}$...
Dmitry Kamenetsky's user avatar
0 votes
1 answer
371 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.
Sny Smartie's user avatar
  • 2,254
1 vote
0 answers
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 ...
Will Octagon Gibson's user avatar
0 votes
1 answer
87 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,...
CSS's user avatar
  • 27
9 votes
3 answers
428 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 ...
Bernardo Recamán Santos's user avatar
-5 votes
1 answer
202 views

Convolution (Literally)

Decode the following message. Hint: Additional hint:
Sny Smartie's user avatar
  • 2,254
4 votes
1 answer
358 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
Anon's user avatar
  • 43
7 votes
1 answer
349 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 ...
user avatar
6 votes
5 answers
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 ...
Ronchen Luo's user avatar
12 votes
4 answers
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 ...
Beastly Gerbil's user avatar
2 votes
0 answers
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 ...
Matsmath's user avatar
  • 1,929
13 votes
1 answer
1k views

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 ...
Bubbler's user avatar
  • 12.2k
2 votes
1 answer
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 ...
Thirdy Yabata's user avatar
0 votes
1 answer
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 ...
Ronchen Luo's user avatar
14 votes
2 answers
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 + ...
LizardofOz's user avatar
18 votes
4 answers
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 ...
Alejandro Garcia's user avatar
9 votes
1 answer
583 views

A puzzle about "someone"

Which symbol is missing? Explain your reasoning.
Prim3numbah's user avatar
  • 32.3k
3 votes
2 answers
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 ...
Bernardo Recamán Santos's user avatar
8 votes
2 answers
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 ...
Will Octagon Gibson's user avatar
1 vote
0 answers
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 ...
Bon Bon's user avatar
  • 11
4 votes
2 answers
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 ...
Olive Stemforn's user avatar
-1 votes
1 answer
234 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 ...
Ali MohammadiNia's user avatar
10 votes
1 answer
915 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 ...
Bernardo Recamán Santos's user avatar
7 votes
1 answer
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.
Will Octagon Gibson's user avatar
2 votes
1 answer
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 ...
Dmitry Kamenetsky's user avatar
16 votes
1 answer
2k views

How does half a dozen remain?

If from six you take nine, and from nine you take ten, (You youths, now the mystery explain;) And if fifty from forty be taken, there then Shall just half a dozen remain. The above puzzle appeared ...
Will Octagon Gibson's user avatar

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