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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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894 views

### Derivative of the coin weight problem [duplicate]

Most people are familiar with the following problem: A well-known example has nine (or fewer) items, say coins (or balls), that are identical in weight save for one, which in this example is ...
144 views

### Who wins the game?

Two people play a game. The first one (A) picks one number from 1 to 10 and then the second one (B) also picks a number from 1 to 10 and adds it to the first number; the next round continues in the ...
32k views

### How can 64 = 65?

Here is a interesting picture with two arrangements of four shapes. How can they make a different area with the same shapes?
15k views

### Nine gangsters and a gold bar

One night nine gangsters stole a gold bar. When the time came for dividing the bar, they faced a problem: two of the criminals put guns to each other's faces. Now it's up to fate whether one of them ...
4k views

### A secret polynomial

Alice has a secret polynomial $P$ with positive integer coefficients. When Bob gives Alice a positive integer $n \neq 2016$, Alice replies with the value of $P(n)$. After doing this several times, Bob ...
4k views

### Eight coins for the fair king

You are responsible for creating new types of coins for the court. King respects the forgetful: he wants you to create 8 coins of different value, no more. King respects the feeble: he wants that any ...
2k views

### Strategy to beat the Casino

Two players, $A$ and $B$, and the Casino play a game. It involves showing zeros or ones: each player picks $0/1$ and also the Casino picks $0/1$. If the Casino and both players $A$ and $B$ show the ...
8k views

### Aside from brute force, how can I solve this puzzle?

Once upon a time, and old lady went to sell her vast quantity of eggs at the local market. When asked how many she had, she replied: Son, I can't count past 100 but I know that: If you ...
14k views

### 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 ...
539 views

### Strategy to beat the Casino reversed

Let's consider Strategy to beat the Casino puzzle, but reverse it - fix number of losses and ask a question about amount of rounds: Two players, A and B, and the Casino play a game. The game ...
3k views

### Fastest way to collect an arbitrary army

I am looking for solution of this puzzle: There is a kingdom with a square shape with sides of length 1. The castle is located at the center of the square. At the castle the king lives under the ...
3k views

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 ...
638 views

### Simple Math Problem #1

Here is a simple math problem. Can you solve it? Examples: 678+57-24*2 = 7 265+34-12*3 = 8 328+58-22*1 = 12 Problem: 541+13-21*0 = ? HINT 1: Will see if this hint makes any sense or will edit ...
50k views

### Make the equation true by only drawing a single straight line

Fred has a puzzle. The instruction sheet, which is separate from the equation,simply says: "Make this equation true. You may ONLY draw ONE, PERFECTLY straight line". The equation is all alone on a ...
1k views

### 99 Bags of Apples and Oranges

You have $99$ bags, each containing various numbers of apples and oranges. Prove that there exist $50$ bags among these which together contain at least half the apples and at least half the oranges. ...
1k views

### A problem circularly coined

I have two coins - one has $N$ times the diameter of the other. I roll the smaller coin one full lap around the circumference of the larger coin like a gear, keeping contact it in with the edge of the ...
805 views

### Dinosaur Egg Drop v2

This question is a little different and kinda follow-up version of Dinosaur Egg Drop 1- You have 100 story building and 6 Apatosaurus dinosaur eggs. 2- You have 81 story building and 3 ...
3k views

### Trapped in my Cellar

I have taken Doorknob hostage in my cellar. He is "perfectly" trapped - solid walls, solid floor, solid roof, no windows, etc. The only way out is a steel door and the only way to unlock the door is ...
1k views

### Deducing Two Numbers based on their Difference and Ratio

Yesterday I met the perfect logicians Divvy and Subtra. I told them: I have chosen two positive integers $x$ and $y$ with $2\le x\lt y\le 100$ and with $x$ a divisor of $y$. I will now whisper ...
4k views

### Will the glass ball break?

Before you stands a building with N-floors. On each floor there is an open window. You have two identical glass balls. If you were to drop a ball out the window onto the ground below, it might or ...
634 views

### Four dice puzzle: 2,2,4,5

Damiano has thrown four dice and the numbers 2, 2, 4, 5 showed up on top. Damiano asks himself: What is the smallest positive integer that cannot be generated with these four numbers according to ...
2k views

### Minimum moves to have all coins face Heads up

Given a circular list of coins, that all have Tails facing up. In each move, if we flip the coin at position $i$, then the coins at positions $i-1$ and $i+1$ get flipped as well. That is, consider: H ...
237 views

### Find the value of $\bigstar$: Puzzle 7 - Boss Battle

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 ...
346 views

### Sub-puzzle: Master and Slave versus Bob the Violent but Honest Psychopath

[I created this as a sub-puzzle to "Strategy to beat the Casino reversed", that has been sitting unsolved for months. You may wish to read that puzzle first, but this is self-contained. My answer to ...
208 views

### Master and Slave versus Bob: easy version

Continuation of: "Sub-puzzle: Master and Slave versus Bob the Violent but Honest Psychopath" Continued in: "Master and Slave versus Bob: hard version" Previously I described a game that is played ...
193 views

### 1984 - take the digits 1,9, 8 and 4 and make 246

Next year is the 70th anniversary of the publication of the book 1984 by George Orwell. Here is a puzzle to start the anniversary celebrations off a bit early ... Warm up Can you assemble a formula ...
612 views

### Wait wait wait wait… 1=0? [duplicate]

Wasn't quite sure if this was suitable for Puzzling; however it has a problem/puzzle in it, so decided to give it a shot. Please appropriately downvote if you feel you should. Yesterday morning I ...
232 views

### A Fairly Simple Riddle [closed]

A homeless man who lives on the streets has a smoking problem. However, since he can not buy cigarettes, he is forced to collect cigarette butts. He needs six butts to make a single cigarette. If he ...
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 ...
6k views

### The Circular Prison of Unknown Size

You are the president of a secret society of mathematicians with $n$ members, including yourself. No one in the society knows what $n$ is. The dictator of the world, in an effort to erase mathematics ...
3k views

### Deciphering an Alien Signal

I have a strange problem that you may be able to help me with. I was recently hired by company that manages several communications satellites, and I've gotten stuck with the overnight shift. Earlier ...
4k views

### Mathematical Rebus

Mathematical Rebus II Mathematical Rebus III  4\sum_{n=0}^{\infty}\frac{(-1)^n}{2n+1}\\ (-\infty,...,-1,0,1,...,\infty)\times(-\infty,...,-1,0,1,...,\infty)\\ \forall\begin{bmatrix}{-1}&{0}\\ ...
4k views

### Filling an 11-by-11 square

Is it possible to fill the $121$ entries in an $11\times11$ square with the values $0,+1,-1$, so that the row sums and column sums are $22$ distinct numbers?
10k views

### How many cars does the millionaire have?

I had a logical riddle on a programming interview test which was something like this: In his garage a millionaire had cars, of which only 2 were not white, only 2 were not green and only 2 were not ...
7k views

### Can the Policeman catch the Thief?

The town of Squareshire has six streets: four sides of a square and the lines joining the midpoints of opposite sides. $\hskip2in$ A policeman is chasing a thief along these streets. If they are ...
5k views

### Teacher, teacher on the wall, Who's the dumbest of them all?

A maths teacher writes a very large number on the blackboard and asks her pupils (of whom there are $n$ in the room) about its factors. The first pupil says, "The number is divisible by 2." The ...
6k views

### Ant walking on a number line

An ant walks on a number line, starting at location $x=7$. Each second, it randomly moves one space either left ($-1$) or right ($+1$), with equal chance. At $x=0$ and $x=10$ are drops of honey; the ...
264k views

### 1 2 3 4 5 6 7 8 9 = 1

This question inspired me to write the same puzzle but instead replace the "= 100" with "= 1" with similar requirements and restrictions. What is the expression with the fewest number of operators ...
5k views

### A Surprising Circle Packing

A grocery store has a long, skinny box, with no top, that it uses to display soda. The box is two soda cans wide and 200 soda cans long. You can neatly fit 400 cans in this box, using two rows of 200, ...
2k views

### Is this 10-card magic trick possible?

A magician (Yes, that's you) has 10 cards, say labelled 0 to 9. Now, the magician's assistant and the magician perform a magic trick: The magician turns around (so he can't see the cards) A volunteer ...
10k views

### A truly amazing way of making the number 2016

Find a mathematical expression that yields the value $2016$ while obeying the following rules: Each of the digits $1,2,3,4,5,6,7,8,9$ is used exactly once Decimal points are allowed You ...
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 ...
2k views

### 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 ...
1k views

### Arrows on a Chessboard

I've taken an $n$ by $n$ chessboard and drawn an arrow on each square, pointing in one of the eight compass directions. I've done this in such a way that arrows in (orthogonally) adjacent squares ...
1k views

### Touching Matchsticks

You are asked to place matchsticks on a flat surface such that each matchstick end meets three others, and no matches cross. It is easy to achieve this for patterns that extend indefintely: The ...
7k views

### How much is the shopkeeper's loss?

A lady buys goods worth 200 rupees from the shopkeeper. The goods were reasonable quality merchandise sold for what the market would bear. The lady gives the shopkeeper a 1000-rupee note. The ...
2k views

There is a highway that starts in the city of Savage. You must must place distance marker signs on this highway for the outgoing traffic. According to highway code, there must be a distance marker ...
A pond contains $24$ waterlilies that are arranged in a rectangular $2\times12$ grid (that is, two rows with twelve waterlilies). One evening $24$ frogs give a croaking concerto for the residents of ...