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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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6 votes
4 answers
411 views

Approximate ln(2) out of small numbers

Given numbers 1,2,...n, the goal of this puzzle is to make a number as close to the mathematical constant $\ln(2) ≈ 0.69314718055$ as possible. Rules You can only use the four mathematical ...
CrSb0001's user avatar
  • 2,423
17 votes
2 answers
2k views

Making a 2n-digit number divisible by 9

Alice and Bob play the following game, taking turns. Alice starts and writes a digit from the set M={1, 2, 3, 4, 5, 6} at the blackboard. Bob appends another digit from the set M until a 2n-digit ...
ThomasL's user avatar
  • 12.2k
7 votes
1 answer
339 views

Can 42 1x2x4 cuboids be packed into a 7x7x7 cube?

Can 42 1x2x4 cuboids be packed into a 7x7x7 cube without cutting any of them? Assume that all cuboids have their axes parallel to the axes of the big cube. I tried using https://www.jaapsch.net/...
mathlander's user avatar
  • 1,261
3 votes
3 answers
265 views

All poker hands from a single deck

This question suggested itself to me – and I found a solution – after I solved Can you balance this poker deck?. Take out two aces from the standard 52-card deck. Your challenge is to partition the ...
Parcly Taxel's user avatar
  • 7,820
4 votes
1 answer
274 views

Can you balance this poker deck?

You are given the digits 0 to 9 in 4 poker suits. Distribute them onto the 8 highest poker hands (make one of each) of 5 digits each. They are Royal Flush (9 to 5 of one suit) Straight Flush (...
Nurator's user avatar
  • 389
13 votes
7 answers
2k views

Fewest number of prisoners needed

You are an assistant to the king, who has scheduled a party tomorrow. There are 1000 wine bottles in the king's possession, and unfortunately, 3 of them are poisonous. Consuming from any of these ...
Durgesh Patel's user avatar
12 votes
1 answer
950 views

Anna tries to make triangles from broken sticks

Anna and Boris play a game with a red stick, a white stick and a blue stick, each of which is 1 meter long. Anna starts by breaking the red stick into three pieces. Then Boris breaks the white stick ...
Will.Octagon.Gibson's user avatar
9 votes
2 answers
295 views

How do I constrain a puzzle and keep a singular solution?

I am tinkering with a puzzle framework that has the following rules: In a 6x6 grid of squares, arrange 8 strips of connected squares such that there exists exactly one strip of every length (i.e. a ...
Brandan's user avatar
  • 143
24 votes
2 answers
1k views

Hexominos from pentominos, heptominos from hexominos

All twelve pentominoes can be obtained by attaching a single unit square (edge to edge) to one of the squares that make up one (or more) of the following four tetrominoes: a) What is the least number ...
Bernardo Recamán Santos's user avatar
-2 votes
1 answer
109 views

How to make all the numbers ranging from 1-30 only using the numbers 1, 5, 0, 4 [closed]

You can use the numbers 1, 5, 0, and 4 but you can't square and cube, you can't use any other numbers, you can't use the numbers more than once, your answer can't be rounded, and you MUST use all the ...
SALAHTHEGOAT's user avatar
4 votes
1 answer
175 views

Curious statements about black cells on a grid

Consider a finite rectangular grid consisting of unit squares (cells). Some cells are colored black, and the rest are white. Some definitions: Two black cells are neighbors if they share an edge. Two ...
Bubbler's user avatar
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24 votes
2 answers
4k views

A pizza dilemma

You are a waiter at a restaurant. The restaurant is known for its signature dish: the Donut Pizza. The Donut Pizza is a 5-inch square pizza with a 1-inch square hole in the middle. After several ...
mathlander's user avatar
  • 1,261
2 votes
1 answer
147 views

Even more interesting equation with fractions

Can you find distinct positive integers $a_1, a_2, \ldots, a_{n-1}, a_n$ for any $n$ such that $$-\frac{1}{a_1}+\frac{1}{a_2}+\ldots+\frac{1}{a_{n-1}}+\frac{1}{a_n} = -\frac{1}{a_1} \cdot \frac{1}{a_2}...
Dmitry Kamenetsky's user avatar
6 votes
2 answers
802 views

Interesting equation with fractions

Find distinct positive integers $a$, $b$, $c$ and $d$ such that $$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}-\frac{1}{d} = \frac{1}{a} \cdot \frac{1}{b} \cdot \frac{1}{c} \cdot\left( -\frac{1}{d}\right)$$ No ...
Dmitry Kamenetsky's user avatar
10 votes
1 answer
986 views

Guess color of your hat cooperatively, goal is all correct or all incorrect [duplicate]

Let n be an integer. n logicians standing in a circle are blindfolded and a hat of either red or blue is put on each person's head. Blindfolds are then removed; each person can now see the color of ...
Lasting Howling's user avatar
4 votes
1 answer
1k views

A puzzle about two coins of total value of 15 cents, one of which is not a nickel. Is it correct at all?

The puzzle: In my pocket, I have two US coins of total value of 15 cents. One of my coins is NOT a nickel. What are the coins? A mathematician told me that I was totally wrong when I posted my ...
Alexander's user avatar
  • 595
13 votes
4 answers
717 views

Pleasant Cuboids

A rectangular prism (or cuboid) made up of xyz identical unit cubes (x along its width, y along its length, and z along its height). Some of those cubes are internal, while the rest are external. Such ...
Bernardo Recamán Santos's user avatar
0 votes
1 answer
161 views

Getting The Numbers 33 Through 99 Only Using 2, 0, 2, and 4 [closed]

How do you get the numbers 33-99 by using the numbers 2,0,2,4
user88484's user avatar
9 votes
5 answers
2k views

Four-cornered cow inheritance

While travelling down a road in a socialist country you meet a group of four young men and women sitting in the front porch of their house, with a lively cattle ranch adjoining. "Our father died, ...
Parcly Taxel's user avatar
  • 7,820
0 votes
2 answers
134 views

A functional equation: Composition to get a... linear function? [closed]

Suppose we have a function such that$$f(f(x))=2x+4\quad\forall x\in\mathbb R$$Does such a function $f:\mathbb R\to\mathbb R$ exist that satisfies the relation, or does such a function not exist?
CrSb0001's user avatar
  • 2,423
3 votes
1 answer
372 views

Place numbers 1 through 9 in boxes (☐☐×☐=☐☐+☐☐=☐☐)

So recently I was scrolling through Youtube when I came across this video from MindYourDecisions that was about solving a legendary math puzzle. The puzzle: Place the numbers 1 through 9 in the ...
CrSb0001's user avatar
  • 2,423
2 votes
4 answers
483 views

Divide rubies and diamonds on a necklace into 2 equal halves

Two thieves steal a necklace consisting of 10 rubies and 14 diamonds, fixed in some arbitrary order on a loop of string. Show that they can cut the necklace in two places so that when each thief takes ...
Hemant Agarwal's user avatar
8 votes
2 answers
423 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
19 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
38 votes
4 answers
3k views

Pythagorean pentagons

To follow up on the theme of so called "pythagorean" dissections, here is one more for you to chew on. I hope you don't get bored. The pentagons above have sides respectively 3, 4 and 5. ...
Florian F's user avatar
  • 30.6k
1 vote
1 answer
202 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
  • 6,033
-2 votes
1 answer
271 views

Circle Point Region Puzzle [closed]

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
17 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
246 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
  • 7,138
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
117 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
1k 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
8 votes
2 answers
452 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
101 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
317 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
  • 7,138
4 votes
4 answers
429 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
6 votes
4 answers
757 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
  • 79
-2 votes
1 answer
141 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
  • 438
-3 votes
1 answer
222 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
503 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's user avatar
  • 3,185
-2 votes
1 answer
173 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
160 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
207 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
5 votes
2 answers
355 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
1k 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
390 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's user avatar
  • 3,185
1 vote
0 answers
60 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

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