# 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.

2,396 questions
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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:
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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?
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### 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 ...
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### 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. $1,$ $1,$ $2,$ ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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,...
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### 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 ...
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### 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:...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...
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, ...