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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18 votes
1 answer
464 views

Seven robot ants that stay forever on a rod

You must place 7 robot ants on a long rod and set each of them to move left or right starting at time 0. You can set any positive speed for each ant. When 2 or more ants meet, they turn around. When ...
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1 vote
1 answer
158 views

Honeycomb puzzle with hexagons [closed]

Can you place the numbers 1 through 9 in the honeycomb so that the sum of the numbers in the adjacent hexagons is a multiple of the number in the hexagons? This must be true in all hexagons. The top ...
6 votes
5 answers
944 views

A peculiar number

A five digit number is multiplied by 9, the resulting number is reverse of the given number. What is the five digit number? This question was asked in KVPY 2020, SA.
  • 1,095
27 votes
2 answers
2k views

Robot ants that stay forever on a rod

You can place any positive number of robot ants on a long rod and set each of them to move left or right starting at time $0$. You can set any positive speed for each ant. When 2 or more ants meet, ...
  • 5,187
4 votes
1 answer
223 views

I’m right 4 times

I can be a 2, or a 4. Split me in half and I can become a 6, but do it wrongly and I’ll be an 8. Lengthen my sides and I am not myself. anymore.
  • 299
9 votes
2 answers
697 views

Pick cards from a table

2022 cards are arranged on the table in front of us. Each card shows a number that we can see. For each of the numbers from 1 to 2022 inclusive, there is exactly one card that depicts it. We have the ...
  • 165
5 votes
2 answers
210 views

Need Thorough Explanation of Coin Weighing Puzzle Solution

One of the coolest things I've seen on Puzzling is this puzzle, and especially the solution in 7 static weighings posted by Julian Rosen. I have revisited that solution many times over the years, ...
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4 votes
3 answers
3k views

Some doctors and a lot of hand shakes

At a congress there are some doctors, and everyone shakes a certain number of hands (never more than once with the same person). The doctors can be divided in two groups: -Group O: the doctors who ...
  • 325
0 votes
1 answer
160 views

Will Romeo meet Juliet? [duplicate]

Romeo and Juliet try to meet each other everyday at a certain place between 12:00 and 13:00. They arrive at the place at a random time between 12:00 and 13:00 and they wait 15 minutes (but never after ...
  • 325
0 votes
1 answer
97 views

How many colleagues went to Starbucks?

You go to Starbucks with some colleagues, everybody gets a cappuccino. Every cappuccino contains only coffee and milk (at least some coffee and some milk) and no other ingredients, but everyone has a ...
  • 325
0 votes
1 answer
120 views

A barrel contains 10l of whiskey, another one contains 10l of coca-cola. If I do the following operation [duplicate]

A barrel contains 10l of whiskey, another one contains 10l of coca-cola. If I do the following operation in two steps: 1 step) with a glass I transfer 200ml of whiskey from the first barrel to the ...
  • 325
12 votes
1 answer
1k views

Patrick and Rachel go to a tennis tournament with 7 other couples

Patrick and Rachel go to a tennis tournament with 7 other couples. Each round is a single's match (1 vs 1). Nobody plays against his/her partner and nobody plays twice against the same player. At the ...
  • 325
0 votes
1 answer
238 views

Sum of digits of numbers

Let S be a function such that S(N) is the sum of digits of N. N belongs to natural numbers, and N < 10²³. N does not contain a zero digit in it. The numbers are in base 10. Find the number of N ...
  • 1,095
4 votes
1 answer
161 views

Tiling twelve 5 x 10 rectangles with ten sets of the twelve pentominoes

I have ten copies of each of the twelve pentominoes. Can I use all of them to completely tile twelve 5 x 10 rectangles?
3 votes
1 answer
317 views

A strange corporate

The employees of corporate "Clocks" have a fixed rule for working hours. All the employees start working at 16:00 and finish their work by 21:00. They take exactly one break during that time....
  • 1,095
3 votes
2 answers
149 views

Productive Neighbours

Seven tiles need to be placed so that one is placed in each of the curved "regions" formed by the three circles. One tile has been placed for you. Each circle has a corresponding statement. ...
0 votes
1 answer
116 views

Mice and their relations

In a colony of $(m n+1)$ mice, must at least one of the following statements be true? If so, why? There is a set $A$ of $(m+1)$ mice none of which is a parent of any other in the set. There is an ...
  • 5,328
3 votes
1 answer
148 views

Find all solutions to a sum of fractions [closed]

Find all the solutions to: $$\frac{1}{x}+\frac{2}{y}-\frac{3}{z}=1$$ where $x, y, z$ are positive integers.
  • 5,328
3 votes
2 answers
163 views

How high does the ladder reach up the wall?

A ladder of length $l$ rests against a vertical wall. Suppose that there is a rung on the ladder which has the same distance $d$ from both the wall and the (horizontal) ground. Find explicitly, in ...
  • 5,328
2 votes
1 answer
84 views

What size square grid can you tile?

A tiling of an n × n square grid is formed using 4 × 1 tiles. What are the possible values of n? A tiling has no gaps or overlaps, and no tile goes outside the region being tiled.
  • 5,328
6 votes
1 answer
165 views

Show there is always a pair at least 16 apart

The integers 1 to 4 are positioned in a 6 by 6 square grid as shown and cannot be moved. The integers 5 to 36 are now placed in the 32 empty squares. Prove that no matter how this is done, the ...
  • 5,328
8 votes
3 answers
1k views

Elegant solution to this digit puzzle

Puzzle The letters $a, b, c, d, e$ and $f$ represent single digits and each letter represents a different digit. They satisfy the following equations: $$ a+b=d, \quad b+c=e \quad \text { and } \quad d+...
  • 5,328
7 votes
1 answer
295 views

Bertrand's Ballot Theorem

A total of X voting papers for candidate A and Y voting papers for candidate B were cast in one section during the election. Where X > Y At the end of election day, the voting papers were counted ...
  • 165
2 votes
2 answers
337 views

Good Rectangles and Evil Numbers

Rectangles and Squares Good Rectangle We define a good rectangle as a rectangle in which $ \frac lw = 3 $ where $ l $ is the length of the rectangle and $ w $ is the width of the rectangle. Tiling ...
4 votes
2 answers
239 views

Can the Spider catch the Fly?

The spider and the fly are both on an infinite line and the spider is hungry. He can move twice as fast as the fly, however his vision is very bad (he can only see the fly when he is 1 meter or less ...
7 votes
3 answers
252 views

How fast do you need to run to catch the bus?

You are running to catch a bus that is going on a horizontal road. The bus is at point (0,0) while you are at point (s,k) where s and k are constants. The bus moves at some velocity v and you have to ...
6 votes
1 answer
327 views

Problem XXX (Squared) - Number Stile

Happy weekend folks, The intersections of the three circles divide their interiors into seven "regions" By complete non-coincidence, we have seven tiles A "valid" placement is one ...
4 votes
1 answer
380 views

Six Different Rectangles

a) Six different rectangles, none a square, have all integer sides chosen from a, b, c, and d. If I take any two of these rectangles with no common side (there are three ways of doing this), the ...
4 votes
2 answers
281 views

Math Crossword with a Twist

This puzzle was inspired by this one Who will be the first to solve this tricky math crossword puzzle completely? Across 2: Half of ({20 Across} x (smallest perfect number) + 446) 3: (Number of ...
  • 17.5k
6 votes
1 answer
447 views

A bunch of circles and squares

The grey region is simply the region you see below. The answer will give you 10 letters. US's: TSDFCK RTOYLG AWQMRZ PUWSTU SRNXEL Hint 1: Hint 2
  • 17.2k
20 votes
4 answers
2k views

Moving around a plane

A small plane went through some heavy turbulence and all its passengers ended up in the wrong seat. Now they need to get back to their assigned seats. The image below shows the map of the plane. The ...
1 vote
2 answers
121 views

What's the correct intuition behind the expected number of die rolls until a 6 if all previous are even? [duplicate]

I came across a puzzle on YouTube recently (spoiler). You roll a fair dice until you get a 6. What is the expected number of rolls, including the roll of 6, conditioned on the event that all previous ...
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16 votes
4 answers
2k views

The Game of Barranca

Barranca is played with sixteen cards, numbered 1, 2, ... , 16. Two players alternately choose a card, until each has eight. The winner is the one who has a (sub)set of numbers whose product is 220, ...
6 votes
2 answers
206 views

Splitting the integers 1 to 36

Split the integers 1 to 36 into two sets, A and B, such that any number in set A has a common divisor greater than 1 with no more than two other numbers in A, but for every number in B there are at ...
12 votes
3 answers
542 views

Find the 3 Famous Numbers

There are 3 clues hidden in the poem below. Each clue reveals a famous number. Find the 3 famous numbers and explain your answer in detail. By. This. I. reveal three clues displaying The relentless ...
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14 votes
4 answers
1k views

The mower's challenge

Weeds have taken over the roads. If mowed, they don't grow back, but unmowed weeds spread at speed 1 along the road. What's the minimum speed of the mower to get rid of all weeds? Roads are connected ...
  • 5,187
3 votes
1 answer
316 views

How many distinct pentominos can be placed on a 8×9 board?

Upon proving optimality of an 8-pentomino solution for an 8×8 board, I was curious to see whether there is a 9-pentomino solution for an 8×9 board, namely a way to arrange 9 distinct pentominos within ...
  • 1,085
14 votes
3 answers
2k views

How many distinct pentominoes are possible to place on an 8 x 8 board?

Rules Place some pentominoes into an 8 x 8 grid. They do not touch each other. They can touch only diagonally (with corner). Pentominoes cannot repeat in the grid. Rotations and reflections of a ...
  • 141
5 votes
4 answers
1k views

Six positive integers

Find six different numbers (positive integers) such that each of them has a common divisor with precisely three of the other numbers. How small can the largest of the six numbers be? What if $2n$, $n&...
1 vote
2 answers
357 views

How many different tiles are there when each corner may have 0-6 dots, each of which may have 0-6 dots?

There are four corners to each tile. Each corner can be empty, or contain an arrangement of dots (1-6) like the sides of a dice. Within each of these dots can be a further arrangement of 1-6 dots, or ...
  • 27
6 votes
2 answers
364 views

How to prove Yin-Yang alternating 2 by 2 is not allowed

Yin-Yang is a puzzle where one needs to fill each cells with either black circle or white circle following these rules: Each color's circles must be connected to one another according to four-way ...
  • 61
2 votes
1 answer
154 views

Hitting twice with different choices

This game of two players has public parameters an integer $n\ge2$, and a probability $p$ with $1/n<p\le1$. E.g. $n=4$, $p=1/3$. In the first phase of a game, a player secretly decides $n$ ...
  • 383
1 vote
1 answer
284 views

Can you escape from two lions?

You're at the center of a circular arena. A pair of lions are at the border, planning to catch you. One of them moves as fast as you, but the other moves slower than you. The three of you are confined ...
  • 5,187
3 votes
1 answer
203 views

Geometric game on a n*n chessboard

You can get famous (OK, Warhol-15 minutes-famous :-)! First a few definitions. Of course, two rooks of the same colors don't attack, but since two colors are needed, "attacking" here means &...
6 votes
2 answers
391 views

Multiplication puzzle with trios of numbers

I created a puzzle that I was curious what its properties are, and how it could be determined it is solvable or not. It consists of 6 rows of 3 of the same numbers, which in each row in order are 1, 2,...
  • 309
15 votes
2 answers
768 views

Can the lion protect the sheep from the wolves?

In a closed arena, three wolves are on the vertices of an equilateral triangle at the border. The sheep and his lion friend are at the center. The wolf eats the sheep if their distance is $0$, and ...
  • 5,187
-2 votes
1 answer
201 views

Summa Cum Laude - Tile and Error

For any set X, {X} denotes the sum of its elements. "I divide {A}" means all items in that set are divisors of the sum of A's elements. Arrange the tiles so that four are in each set and the ...
0 votes
4 answers
180 views

Solve for 69 using only 1 9 9 2 in that order [closed]

You must use all the digits of $1 9 9 2$ in that order to come up with $69$ as the answer. For example $ - (1 + \sqrt {9})! + 92 = 68 $ but you must solve for $69$.
1 vote
0 answers
68 views

Riddle: Irregular math [duplicate]

A numbery riddle: When I take five and add six, I get eleven, but when I take six and add seven, I get one. What am I? What is the answer?
4 votes
1 answer
281 views

SETI message received

At 03:39:18 UTC, the Allen Telescope Array detected a series of distinct signals from the direction of the Procyon star system. There is speculation that these signals considered together could carry ...
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