# 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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### 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 ...
73k views

### Make numbers 1 - 30 using the digits 2, 0, 1, 8

It's 2018 so let's repeat last year's challenge with new digits. This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 8. Rules: Use all four digits exactly once Allowed ...
6k views

### Variation of 100 prisoners light problem

There is a classic problem below for which Dr. Yisong Song wrote a very well written and thought out series of solutions. The variation here I've never seen anywhere but am curious. I want to work it ...
3k views

### How to choose at least half of everything

Some number of gold, silver, and copper coins are scattered in $N$ chests. You may look into each chest and count each type of coin in them, and then select $M$ of the chests. Your goal is to have at ...
977 views

### How much money can we make?

My five friends and I used to loan each other money all the time. But over the past several years we have moved apart. We don't trust PayPal, banks, or the postal service so transferring money over ...
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 ...
746 views

### The answers to these questions are?

C is the correct answer to how many questions? A. 1 B. 2 C. 3 D. 4 Which letter is the correct answer fewer times than any other? A. D B. B C. C D. A Which letter is the ...
1k views

### Welcome to Oɴᴇderland

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...
549 views

### The life of a Knight: Conway style

So I was thinking about Conway's game of life and the ridiculous kinds of patterns that can be made (Things that move across infinite space etc) and then I thought, hey could a chess knight do this as ...
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### Make 5 5 5 5 = 19 [closed]

Can you find a way to make: $5\ 5 \ 5 \ 5 = 19$ by adding any operations or symbols? You can use only these symbols: $+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$. It is limited to this list, and ...
6k views

### How many diamonds? [duplicate]

A group of Seven men robbed a diamond shop at night. They ran to a nearby forest and all slept there for the night. One of them woke up and tried to run away with the bag full of diamonds, but ...
6k views

### Google's 20th Anniversary: Make 20 using 6 0 0 6 1 3

Belated 20th Happy Birthday to Google (600613)! Challenge: Use 6, 0, 0, 6, 1, 3 to make the number 20. Rules: Use all numbers, in that exact order. Allowed operations: +, -, x, /, sqrt, (); no ...
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### 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 ...
3k views

### How many flowers to buy? [duplicate]

A man decided to place some flowers on three different temples. There is a magical pond before each temple and he has to swim through each one. So his trip will be: [ pond1 - temple1 - pond2 -...
3k views

### Worm and an Apple

Johnny has a perfectly spherical apple, with a diameter of 70 mm. While he looks away, a worm burrows through (entering and leaving) the apple, forming a single tunnel of length 69 mm and negligible ...
4k views

### bored of eating soup

A man orders spicy noodle and leek soup from a restaurant, but gets bored while eating. When he gets bored, there are exactly 100 noodles in the soup. Because he is bored, he decides to play a game ...
2k views

### Which data file is genuine?

NASA has spent hundreds of millions of dollars gathering data about cave systems in one region of the planet Mars. The project just finished up, and analysts will soon be ready to start analyzing the ...
1k views

### Musical in Nature

What is the next song in the list? Pedal To The Medal Not Inside -- Outside The Final Countdown Every Rose Has Its Thorn ......... The Puzzle Within these dots, you shall find a magical, mystical, ...
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### 3 Numbers on Hats, A = B + C

This feels like it should be a common puzzle, but I haven't found anything exactly like it searching online, so here goes. Apologies if it's a duplicate. Three logicians, person 1, 2, and 3, along ...
2k views

### A few Mathematicians derived from formulae

Find the 3 mathematicians which may be revealed, with a little manipulation, from the formulae below. They are well known enough to be in the MacTutor History of Mathematics archive. \frac{\chi }{...
1k views

### Powers of two my children be

Powers of two my children be, Arriving in birth years separately. Their sum is now the reverse of me And the years between me and a power of three. My digit difference is the number ...
3k 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 ...
106k views

### Five Angles in a Star

In a regular pentagram (5-pointed star), the angle in each point is 36 degrees, so the angles in all five points sum to 180 degrees: What about an irregular pentagram, such as the following? Now the ...
6k views

### Picking up stones

Here is puzzle that was lifted from an old essay of mine, that was adapted from a puzzle in an old puzzle book. The great shah has invited a young boy into his palace as a student. While he is not ...
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### A magic trick of David Copperfield

David Copperfield puts $52$ cards numbered $1$ to $52$ into three top hats. One of these top hats is red, one is blue and one is yellow, and each of them receives at least one card. Then David ...
3k views

### Robots in a spaceship

Xerxes has 6, 7 and 8-arm robots in his spaceship. Unfortunately, the 7-arm robots are misprogrammed and everything they say is a lie. The other robots are fine, they always speak the truth. Once ...
15k views

### Get 100 as an answer on a calculator without using 0

Task Get 100 as an answer with only four keystrokes on a regular calculator. Disallowed keys 0 00 Allowed keys All other than the aforementioned two keys. Take the below image as a reference. ...
2k views

### Digging a tunnel between random locations

Romeo and Juliet are each placed uniformly at random locations on a spherical planet, meaning that each square meter of surface area of the planet is equally likely. Romeo decides to dig a straight-...
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### A game with 52 cards

Alice and Bob play the following game with two (identical) standard decks of $52$ cards. First Alice secretly arranges one deck of $52$ cards in a long row on the table. All cards are face-down, and ...
2k views

### How much water do you need to cross the desert?

This question is inspired by Terry Pratchett's "Small Gods," in which an army crosses a vast desert by making multiple trips and caching water along the way. 1. Provide an answer. 2. I doubt I'm the ...
3k views

### Ten Tricky Mathematicians

Somewhere on the Hyperbolic Plane, you encounter ten mathematicians. You know that some of them always tell the truth while the rest always lie. Each of them knows which of the others tell the truth ...
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### A Bridge Problem

You are on the North Shore of a river, and you want to get to the South Shore. In the river are 6 islands and 13 bridges connecting the islands and shores. However, a storm gives a 50% chance to each ...
1k views

### Checkerboard Infection: The Aftermath

As in this previous puzzle, we are again playing with our favorite bacteria, C. Coli, whose natural habitat is an 8x8 checkers board. These are very nasty bacteria - once they are in a cell of a ...
1k views

### Four points with only two distances

Your task is this: Find all arrangements of four distinct points in the plane such that only two distances occur between them. When you have $4$ distinct points, you can measure the distance ...
867 views

### The year 2016 is approaching

Do there exist integers $r,s,t\ge100$ such that the decimal representation of $(r+\sqrt{s})^t$ is of the form $~~~\ldots\ldots2015\,.\,2016\ldots\ldots$? (In other words: the four digits before the ...
3k views

### The LoL number game

Tim and Tom are fictional characters (cats, I believe) who like to play the LoL number game. In this game, Tim chooses two distinct integers A and B, both ≥ 2, and shows them to Tom. Tom's goal is to ...
1k views

### Unexpected Delay while Mixing Shots

You are hosting a party, and everything is going perfectly well, until you ask if anyone wants a kuulalaakeri shot. (In case you are not familiar with this highly treacherous Finnish beverage, it has ...
3k views

### Winning an unfair game

I came across the following interesting problem today: A game consists of a sequence of plays; on each play either you or your opponent scores a point, you with probability $p < \frac{1}{2}$, he ...
620 views

### A table filled with greatest common divisors

Yesterday I met professor Halfbrain at an art gallery. The professor told me that recently he had been spending his time with constructing $n\times n$ tables for integers $n\ge3$: the entry at the ...
510 views

### From zero to parabola in 14 symbols

Post up, weekend analytic geometers, get ready to race for the parabola and approach the starting line with 0 and 7 other symbols:       0   =   ( ...
375 views

### Orange you glad it's not Lemon?

My friend gave me this note in class, my very own third grade mathematics class! But alas: To little, my third grade-ly efforts amassed. Again and again, I wish I'd known then,...
1k views

### Monte Carlo Chess

This is an entry to the 17th fortnightly topic challenge. Chess is an interesting game, but is so unrealistic. In real life, you couldn't tell order your knight to attack an enemy bishop and expect ...
770 views

### Master Bomb Defusers

Day 115 of your investigation and you and your ever-faithful-if-only-a-bit-slow partner have finally caught the trail of your arch-nemesis, a serial bomber known only as "Mr. 5". Doing your best to ...
8k views

### What's the largest number you can spell?

If I give you one of each letter in the alphabet what's the largest you can spell (in word form)? Bonus: What's the smallest? Bonus 2: What if you can use the words "minus", "plus" and "times"?
5k views

### Hidden in plain sight - By what method do these images hide a prime number?

Note: This question has been severely edited from its original version to better fit the format of this site. Some answers below - including the accepted, correct answer - have been given based on the ...
3k views

### Simple Maths Riddle 2

I have a definition, but I'm not literally defined. The simplest of shapes: circles and lines. A decimal you'll require; my anagram leads a choir. What am I? HINT 1
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### 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)...
3k views

### A rectangular room has a floor tiled with tiles of two shapes: 1×4 and 2×2

A rectangular room has a floor tiled with tiles of two shapes: 1×4 and 2×2. The tiles completely cover the floor of the room, and no tile has been damaged, or cut in half. One day, a heavy object is ...
Yesterday I met professor Halfbrain at the coffee house. The professor told me that he had been spending his time with computing powers of $2016$ and combining them with powers of $32$. The professor ...