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Questions tagged [mathematics]

A puzzle strongly related to mathematical facts and objects, or whose solution needs serious mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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7
votes
4answers
293 views

Savage Road Signs (Part 2)

Please read part 1 or this might be confusing Since part 1, you have replaced the stolen stickers and your daughter has forgiven you. The highway ended up being a full 700km long, so you are happy ...
6
votes
3answers
733 views

Mathematical Rebus III

Mathematical Rebus I Mathematical Rebus II Small note on the first image: Hint 1 for the squares image: Hint 2 for the squares image: Hint 3 for the squares image (alternative image that should ...
6
votes
1answer
487 views

The square and the compass

(I don't mean $x^2$ or $N\cdot S\cdot E\cdot W$) You have a compass and a pencil but no scale/straightedge. Your job is to mark four points on a plane paper that would form a square if joined. Your ...
6
votes
1answer
133 views

The town of Concentrië

Here you see a water map of the town of Concentrië. There are eight channels that run from the central boathouse of the city in a star shape. There are three canals that lie concentric around the ...
6
votes
3answers
2k views

Coloring an n by n grid with four colors

This is a generalization of Place 4x12 detainees on a 7x7 grid of cells. The goal is to color the squares of an $n\times n$ grid with four colors such that at most one square is uncolored no two ...
5
votes
3answers
863 views

The Great Houdini's awesome card guessing trick (1)

The Great Houdini is performing again! A guy from the audience arbitrarily chooses $52$ cards from a huge stack. He shuffles the cards and announces to Houdini that there are $a$ spades, $b$ hearts, $...
4
votes
1answer
190 views

Three-digit multiplication puzzle

Place different three-digit numbers (000-999) on each of the seven nodes of the following diagram: There are six lines in the diagram, on each of which are three of the nodes. On each of those lines, ...
4
votes
2answers
920 views

Island inhabitants: Who lies and who tells the truth? [duplicate]

On some island, the population is split into native people and into outlanders. There are more natives than outlanders. Someone with extreme logical and mathematical thinking wants to know who are ...
4
votes
3answers
1k views

The bird and the train

This question is one I found in a competitive exam paper, and has two solutions: one simple and one complex. A train starts from the east end of a 200 km long east-west track at 50 km/h. At the same ...
4
votes
1answer
955 views

Odds of duplicate birthdays

I found the following problem in an number of places online: John once bet a fellow gambler that two of the first thirty persons they met and spoke to would prove to have the same birthday. Strong ...
3
votes
2answers
163 views

Pigging out in proportion

My batty and quite senile great-grandmother (on my wife's side) left me a fish and chip shop in her final will and testament after she was beheaded for treason (...long story). The executioner of the ...
2
votes
2answers
203 views

Magical Knight Moves with Effortless Ease in his Magical Kingdom

Magical Knight knows every Square of his Magical Kingdom. In many respects, he is like any other knight...Literary,Prime, Normal(makes same allowed chess moves). He is people Knight . As he traverses ...
2
votes
4answers
1k views

Time to speed up [closed]

Mr. X lives in A-City and wants to visit B-city. There are 1000 km between these 2 cities. So, Mr. X takes his car and drives to go to B-City. At halfway of his ride (500 km), he realises that his ...
1
vote
1answer
180 views

Find the value of $\bigstar$: Puzzle 8 - Inequality

This puzzle replaces all numbers 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 down, I recommend you solve Puzzle 1 ...
1
vote
2answers
257 views

The n coins and the scales [duplicate]

The other day I was reading a puzzle book and found this classic: There are 9 coins on the table, but one of them is fake and weighs slightly less (or more, doesn't matter). How many measures do you ...
0
votes
2answers
1k views

6 Attempts to Guess a Number Between 1-100 ~ Ranges

You get get 6 attempts to find the number between 1-100. Each "attempt" can either be a guess, or a range it could fall in, responses you could receive are "Correct!", "My number is lower.", "My ...
-2
votes
8answers
25k views

Can you solve this? Answer isn't 19 or 26 [closed]

I've found this viral image online, can you solve it? It is tricky, but simpler than you think. Source: Originally found it at CBP - Brain Centers Facebook Page.
-2
votes
2answers
739 views

Bridge's riddle [duplicate]

You're in a group of people going for an internship in a remote mountain lab. By mistake you pulled a lever with a skull just out of curiosity and it released some zombies. So you and your group had ...
-3
votes
2answers
427 views

When will the bacteria fill the test kit? [closed]

A test kit, is a gathering place for a colony of bacteria. This Colony, at 12 pm cell division has created a bacteria. Every minute, every bacteria is divided into two bacteria. 12: 43 (43 minutes ...
-5
votes
2answers
798 views

Magic square using consecutive odd numbers -5 through 11

Using consecutive odd numbers from negative five to eleven, make a 3x3 magic square
51
votes
3answers
3k views

The Case of the Miscalculating Calculator

At the Arithmetic Company, to try and cut down labor costs the administration commissioned a calculator to be made. The calculator was produced, and in the quality control division was tested with the ...
62
votes
7answers
10k views

Three mathematicians are forever in Prison

I'm excited to share the following riddle. It was given to me more than two years ago and I finally solved it last summer (after not thinking about it for a long time). In my desperation, I tried to ...
44
votes
7answers
9k views

How many tries to roll a 6?

Suppose you roll a (fair, 6-sided, perfectly ordinary) die repeatedly until you roll a 6. As is well known, the expected (i.e., long-term average over many trials) number of rolls required is 6. Now ...
76
votes
10answers
17k views

10 Prisoners, 10 Keys, and 7 Years

One day, the warden of a prison is, like most wardens in puzzles, feeling a little bit capricious and decides that he wants to get rid of his prisoners, one way or another. He gathers all the ...
45
votes
7answers
13k views

Does the drunk man fall off the cliff? (a random walk problem)

A drunk man stands with a cliff one step to his left. He takes steps randomly left and right. Each step has probability $p$ of going left and probability $q=1-p$ of going right. Each step is the same ...
32
votes
11answers
3k views

Coin weighing with a single weighing device

You have 12 coins which each weigh either 20 grams or 10 grams. Each is labelled from 1 to 12 so you can tell the coins apart. You have one weighing device as well. At each turn you can put as many ...
26
votes
3answers
2k views

Unsolved Mysteries: Magic Square of Squares

This is the first in what will hopefully be a series of Unsolved Mysteries posts. Note that this puzzle has no known solution, nor any proof that a solution is impossible. We will see how ...
62
votes
24answers
20k views

Make 0 0 0 0 = 8

Can you find a way to make: $0\ 0 \ 0 \ 0 = 8$ by adding any operations or symbols? You can use only these symbols: $+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$. It is limited to this list, and ...
27
votes
10answers
3k views

One prize, infinitely many choices

Having reached the final stage of a game show, you face an endless row of doors labelled $1$, $2$, $3$, ... The game show host has selected a whole dollar amount, and has put this exact amount as a ...
15
votes
6answers
718 views

A triangular Quidditch field

A Quidditch field is usually in the shape of an oval, a hundred and eighty feet wide and five hundred feet long. But today the Gryffindor house team is training on a smaller field in the shape of a ...
62
votes
8answers
17k views

A walk of 3000 meters, but one foot has moved more, how so?

My math teacher has struck again. Here's his newest riddle: Today I went for a normal walk of 3000 meters. One of my feet had to move exactly 3000 meters. However, the second foot moved 3100 ...
41
votes
2answers
5k views

Ten numbers on a blackboard

The numbers 1 through 10 are written on a blackboard. You erase two numbers of your choice, and write their product plus their sum $$a,b \to ab+a+b$$ So, now there are nine numbers on the board. You ...
36
votes
6answers
3k views

The subtraction game

Alice and Bob play a game that starts by Bob picking a secret integer $N\ge100$. Then the game goes through several rounds. In every round, Alice picks an integer $x\ge3$. Every number can be picked ...
33
votes
9answers
4k views

Thirty genuine and seventy fake coins

In the country Curgonia, there are many types of fake coins and only a single type of genuine coins. The weights of these coins satisfy the following conditions: All genuine coins have the same ...
24
votes
3answers
1k views

The PSE School of Enigmatics (Part 1)

Update: I fixed up the second image, making it (perhaps) a little bit easier to crack. You leap out of your bed. Today's the day! You check your mailbox, and wow, there it is! The frayed look of the ...
18
votes
8answers
2k views

30 fake coins out of 99 coins

You are given 99 coins which consists of 30 fake ones. You also have a digital balance scale with perfect precision that shows how much difference between weighs you put on. For example, if you put 10 ...
21
votes
6answers
6k views

3x3 “Magic Square” of Prime Numbers

During the thinking and analysis of some mathematical problems, I came up with this puzzle: Just like any magic square, one has to fill in $9$ different numbers $P_1, P_2, \dots P_9$ to a $3 \times 3$...
19
votes
4answers
1k views

Magician's hide and seek with 8 cards

This question is a followup to this question by @Wen1now. After demonstrating the previous trick, the magician decided to make things a bit harder, discarding some cards so that only eight were left. ...
-1
votes
14answers
2k views

Move one thing in the equation [closed]

$1484 / (7 / 9) = 19$ Make the equation true by moving one continuous shape or operation in the equation.
33
votes
2answers
746 views

lolcatz can haz ur infinit cheeseboard

This is a problem on an infinite chessboard with pieces called lolcatz. They can move like queens or knightriders, but have a strange disadvantage... ... you've never heard of knightriders? Well, ...
32
votes
3answers
3k views

The Determinant Sudoku

The determinants of $2\times 2$ matrices are calculated this way: $$\det\begin{bmatrix}a & b \\c & d \end{bmatrix}=ad-bc$$ And here's the sudoku-determinant puzzle: What's the solution for ...
32
votes
8answers
6k views

Will the ant reach the car?

A car starts distance 1 from a wall then drives away at constant speed $ c $. There is a length of elastic tied between the wall and the car. Remarkably this doesn't affect the motion of the car (in ...
26
votes
4answers
2k views

This image contains a “Great Discovery”

The Puzzle: Source material taken from here As discussed on Numberphile, here is John Herschel's doodle, sent to his friend Charles Babbage. John H. John Herschel was an English polymath, ...
26
votes
2answers
2k views

Unknown weight of four identical objects

Four identical looking objects weigh 3oz, 5oz, 8oz and 11oz. You do not know which objects weigh what and they are too close in weight to tell by holding them. Using a balance scale, how can you ...
23
votes
3answers
2k views

Gambling in a rigged casino

A well-known crooked casino is offering the following bet with a pair of (identically looking and indistinguishable) dice that both show the numbers $1,2,3,4,5,6$ on their faces. The first die ...
23
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3answers
1k views

Welcome to Oɴᴇderland

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...
17
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2answers
2k views

Game of Drones - Zap it!

Your programmable drone is pitted against another drone in a rectangular 3D arena measuring 40 meters long, 40 meters wide and 20 meters high. You have equipped your drone with a laser gun that will ...
12
votes
3answers
1k views

Which Flight Takes Me Home?

My vacation just ended, and I'm at the airport headed back home! It was definitely an enjoyable trip, but it could also be described as, well, unusual. I've got a more immediate problem though. I've ...
39
votes
22answers
8k views

Aproximating 100 by 6

You're a fan of pen & paper RPGs and have finally arranged a new playing group, recruited amongst your friends from the mathematical faculty. As a GameMaster (GM) you've assumed that all your ...
32
votes
4answers
2k views

The Devil's Brother

The 1933 movie "The Devil's Brother" (also known under the title "Fra Diavolo") takes place in the Northern Italy of the early 18th century. Stan Laurel and Oliver Hardy play the fierce robbers ...