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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.

17
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3answers
2k views

Baggage Problem: $1.5$-meter-long sword onto a train

This is the problem I came across reading the book The Art and Craft of Problem Solving. When I read this question I wasn't able to figure out the solution and I saw the solution after a while, but ...
7
votes
2answers
2k views

Can you help the traveller

A traveller decided to explore a square desert. He started from a point on the edge to point B, travelling perpendicular to the edge of the desert he started on. On reaching B, he then decided to take ...
0
votes
3answers
856 views

Inheritance by cards [duplicate]

An old farmer passes away in his sleep. After a suitable period of mourning, his three sons find their father's will in his study. Amongst other, simpler bequests is the following: "I wish my small ...
4
votes
1answer
388 views

Housing crisis in heaven

Heaven has a countably infinite number of cloud for people to stay, each of which has a good soul living on it. A countably infinite number of infinite universes are extinguished by God (their beta ...
21
votes
4answers
2k views

Ernie's Clockwork Calculator

I was helping Ernie clean out his shed a while back when I saw a curious old machine. "Oh yeah, that!" said Ernie, when I pointed it out to him. "A few years back, before transistors were invented, I ...
3
votes
5answers
938 views

A belt, a stone and a wooden stick

We're on the middle of the most devastating war the Earth has gone through all its history. You and your brother in arms are in a plane that has been taken down while crossing the enemies lines. You ...
-6
votes
3answers
927 views

When Math Loses Meaning

In an alternative universe where the following is true: 1 # 1 = 3 2 # 2 = 7 1 # 2 = 5 What would ? be? 5 # 5 = ? YOU DO NOT NEED THE FOLLOWING TO FINISH. Extra equations:
5
votes
1answer
2k views

Generalization of Sum and Product puzzle

I heard from a clever person that for the problem mentioned before: I don't know the two numbers... but now I do a solution exists even if we change 100 to infinity. So the formulation would be ...
2
votes
2answers
844 views

100 sequential parking spaces

I just came up across this question in the mathematics stack exchange site and found it quite interesting: 100 autonomous robotic vehicles enter a warehouse in random order to park. Inside the ...
41
votes
17answers
8k views

A blanket for my baby snake

Mama snake wants to knit a blanket for little baby snake. She is not a dissipater and wants to make the blanket of a minimal size (area). But her baby snake is quite a lively baby and it always ...
1
vote
3answers
990 views

How many equal-sized polygons can be used to cover a soccer ball?

It seems that mostly either 26 or 32 equal-size polygons are used to cover a spherical soccer ball. What other configurations are possible?
118
votes
8answers
19k views

The Sheikh dies

The Sheikh dies, leaving behind three sons, 17 camels and the following order: His oldest son shall inherit one in two camels. His middle son shall inherit one in three camels. His youngest son shall ...
6
votes
3answers
2k views

Amount of hair on the head

Can you prove in two different ways that at this moment, some two persons on Earth have exactly the same number of hairs on the head?
4
votes
3answers
543 views

Flowers For a Patient

A woman wanted to visit her friend at the hospital. She had walked 500 meters from her front door before remembering that she wanted to pick up some flowers. She went back to the florist she had ...
6
votes
3answers
965 views

What is the next 3 numbers?

These numbers are created with a formula. Guess the formula for increment and calculate at least 3 next numbers of this sequence. increment is started with two given first $1$s. $1,$ $1,$ $2,$ ...
10
votes
1answer
2k views

20 coins on the table

Two boys , Brian and Gabe, decide to play a game. They lay 20 coins on the table. Each player took turns taking 1, 2, or 3 coins. Whoever took the last coin won. Brian thought if he went first, he'd ...
32
votes
3answers
5k views

Do better than chance

You and an opponent are playing the following game: Your opponent picks two different real numbers, however he wants to, and writes them on two cards, which he presents to you face down You choose ...
6
votes
2answers
2k views

Find the age of the ship and of the boiler

Some years back I was travelling by a cargo ship from New Zealand to Tahiti. I was curious to look around the ship one day and in the boiler room I asked a man how old the ship was. He smiled and ...
1
vote
3answers
457 views

Balance the Equation

Peter found an old piece of paper that an equation was written on it. Some of digits or operations are unreadable. Help Peter to complete the balanced equation. The equation is: $87+?3?12-4?2=?36-15??...
7
votes
1answer
399 views

Shortest time interval measurable via burning a rope

You are given some matches, a rope, and a pair of scissors. The rope burns irregularly and takes 60 minutes to burn end to end; however, we know that the burn rate at distance $x$ from the left end is ...
16
votes
1answer
3k views

The Laziest Surveyor

The new land surveyor and his boss arrived at the work site, a huge and perfectly flat parking lot. His boss said, "Your first assignment is going to be a tough one. You see this parking lot? It ...
12
votes
2answers
1k views

How to ship the new Slurm 7-pack efficiently

The six-pack is a thing of the past. Beverages of the future will use the seven-pack format. But how will the mighty spacemen of the future manage to ship the Slurm seven-pack efficiently in ...
6
votes
1answer
2k views

What is the number 4.9292683…?

Guess the next digits of this number. Where does it came from? 4.9292683
-3
votes
2answers
651 views

Infinite Troll Tolls

So, recently there was a very good riddle posted here: Paying the Troll toll. I would like to propose a similar question which might have been partially answered. But anyways... So, same basic idea ...
5
votes
3answers
827 views

Witches and Cats

This being Halloween, we will consider the problem of witches and their cats. The whole crowd is out tonight, naturally, and an interested observer, seeing them fly by (yes, witches' cats fly), ...
6
votes
2answers
528 views

Odd birthdate surprise

Last year, just before my birthday in February, I noticed something unsual. The last two digits of my birth year were the same as my age. How old was I then and was this an unusual occurrence?
13
votes
2answers
989 views

Horses and Tracks

I have seen this question before and I am intrigued that there might be various ways it can be solved. I do know of one way, but I am trying to find out if there is any other approach possible. The ...
147
votes
1answer
7k views

Chaos and Order: a visual puzzle in stained glass

I created a visual puzzle, which my wife then implemented as part of a stained-glass window. I've no idea if it is (a) obvious, (b) stupid or hopefully (c) extremely clever, and hence would love to ...
15
votes
2answers
764 views

Santa Claus flies to the South Pole

It is a little known fact that Santa Claus is in fact a vampire. Why else would he spend so much time near the North Pole and travel only at night? Yes, he fears daylight! His problem is that ...
-1
votes
1answer
448 views

Products of three primes that bound RSA numbers [closed]

Let $N$ be some number. Let $R$ and $S$ be semiprimes [ie, each is a product of two prime numbers] such that $R \le N \le S$. For quite a few numbers $N$ we can find $R, S$ such that $S-R$ is small;...
9
votes
2answers
1k views

Entangled physicists

The anti-intellectuals have won the war, and under the iron rule of emperor Nonotin anyone who has been deemed too smart for their own good has been brought to labour camps. But most of the science ...
-2
votes
1answer
684 views

Find the Different Sugar Cubes [duplicate]

There are 10 Boxes, each contains 1000 sugar cubes. The sugar cubes in 9 of the boxes are 10 grams each and the other box has 9 gram cubes. There is a digital scale that you can use it ONCE. (i.e. ...
3
votes
2answers
1k views

Unknown Consecutive Integers Puzzle

Two people, Anne and Bob, each hold an index card. A positive integer is printed on each index card, and these integers are consecutive (i.e. Anne's card may display 8 and Bob's card 7). Anne and Bob ...
20
votes
4answers
3k views

The Monty Hall problem

I'm amazed that, although well known, this problem hasn't been posted yet. Monty Hall You are on a game show. The host of the show shows you three doors. He tells you that behind one of them, is a ...
20
votes
3answers
5k views

The lake monster

You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can't swim. He can run (along the perimeter)...
9
votes
2answers
533 views

Generalizing the “shooting puzzle”

Inspired by this puzzle. You have $n$ shooters having a duel, labeled $1, 2, ... n$. Each shooter has an accuracy of $k_n$, with each $k_n$ some probability in $(0,1]$, with $k_1 < k_2 < ... &...
3
votes
2answers
506 views

Find a high-scoring 53-digit prime number chain

Let a “number chain” be a series of numbers, $n_0, n_1, ... n_{m-1}$ for some $m$, such that in base 10 the low digits of $n_i$ match high digits of $n_{(i+1)mod m}$. For example, after the number ...
5
votes
7answers
6k views

Help understanding the solution to a “shooting puzzle”

I need help understanding the solution to the following puzzle: Puzzle: There is a "triangular" duel between the three shooters. Everyone shoots one by one, can shoot once and any person he wants. ...
3
votes
2answers
1k views

Find shortest network connecting four points

Given the figure below, find the shortest network of straight line segments (like a Steiner tree, or like parts of a Delaunay triangulation) that connects the four circled points while staying in the ...
17
votes
3answers
2k views

Fair results with unfair die

You are given a 6-sided die.The die is biased, so it is more likely to produce some results than others, but you don't know the exact odds. It is however given that the odds are the same for each roll,...
4
votes
2answers
1k views

Markus' lucky numbers

It was late night when Markus was sitting at his desk and suddenly a fairy appeared out of nowhere. She told him that he had been granted a wish. Markus wished for her to tell him next week's lottery ...
5
votes
2answers
906 views

Theoretical Puzzle: Making a binary puzzle with a unique solution

If I have a table of binary values, and tell you the column and row counts for "on" or "1" values, is it possible to solve, with certainty, any grid of size n*m? Take the following puzzle for example:...
7
votes
8answers
3k views

Divide 3 cakes into 4 equal parts?

You have three cakes of diameter 20cm, 16cm and 12cm respectively as shown in the figure. They all have the same height. Now your task is to divide these 3 cakes into 4 equal parts and you are ...
6
votes
1answer
688 views

Unlocking a curiously-geared combination lock

The image shows numbers on ring-dials on a curiously-geared combination lock, where the current setting is (3,3,3,3) and ring sizes are (5,7,8,11), inner to outer. The setting (0,0,0,0) opens the ...
10
votes
3answers
4k views

Mirrored numbers

If you multiply $2178$ by $4$ you will get the same digits, but written in the back order, like if you look in a mirror: $2178 \cdot 4 = 8712$. How to find all possible natural numbers, that are ...
2
votes
1answer
266 views

Guess the Function for Scatterplot of Number Theoretic Function

To my knowledge, this puzzle is not previously published (except by me on google+ recently), but I would be interested to hear of any info otherwise. This following graph was generated using a simple ...
1
vote
2answers
387 views

Bottle rinsing with fixed amount of wash water

Given $L$ units of wash water, we want to wash out a vessel (eg, a milk bottle, honey jar, chemistry flask...) using a series of rinses that minimize the amount of Stuff other than water remaining in ...
18
votes
4answers
2k views

The 8-dimensional vegetable kebab

You are given two of each from the array of 8 vegetables numbered 1 to 8 as shown above. So in total you have 16 veggies(8 pairs). Your task is to make the longest kebab (sequence of vegetables ...
9
votes
2answers
428 views

A Martin Gardner problem about constructing a scoreboard given minimal information

The following is a paraphrasing of a problem from Martin Gardner called "Tricky Track." Three schools $-$ $A,B,C$ $-$ participated in a track meet with several events. Each school was awarded some ...
6
votes
1answer
481 views

Arranging cards in rows

This question appeared in an old math contest, and I seem to remember that the answer I had back when I first saw it was unsatisfactory. You have a deck of cards numbered from $1$ to $60$. First, ...