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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1answer
849 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 ...
125
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8answers
31k 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?
63
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3answers
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 ...
35
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5answers
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 ...
29
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7answers
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 ...
22
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10answers
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 ...
13
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3answers
526 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 ...
12
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7answers
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 ...
25
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10answers
3k views

Make 2 dice out of 3 dice

This question was first posted by standupmaths on youtube: https://www.youtube.com/watch?v=xHh0ui5mi_E He already got some answers but I think this community can probably find a better answer. ...
18
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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 ...
10
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1answer
637 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 ...
25
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4answers
47k 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 ...
12
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5answers
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. ...
7
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3answers
799 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 ...
19
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6answers
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 ...
14
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1answer
3k views

How do you solve the circular table problem?

One classic puzzle has many different forms, but the basic strategy is the same. Once upon a time there was a crazy king who had a very wise minister with him. The king had a habit of playing a ...
11
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1answer
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 ...
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8answers
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 ...
8
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2answers
624 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 ...
6
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2answers
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 ...
4
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2answers
232 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 ...
0
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3answers
325 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 ...
2
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1answer
189 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 ...
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1answer
180 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 ...
-2
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2answers
610 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 ...
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3answers
229 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 ...
149
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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 ...
79
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18answers
14k 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 ...
44
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7answers
5k 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 ...
47
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6answers
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 ...
38
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6answers
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 ...
51
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1answer
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}\\ ...
36
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9answers
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?
31
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8answers
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 ...
67
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5answers
6k 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 ...
30
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13answers
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 ...
27
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19answers
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 ...
14
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12answers
261k 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 ...
36
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7answers
4k 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, ...
13
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16answers
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 ...
21
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6answers
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 ...
21
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7answers
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 ...
25
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4answers
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 ...
14
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3answers
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 ...
12
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11answers
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 ...
24
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4answers
2k views

Savage Road Signs

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 ...
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4answers
1k views

The frog concerto

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 ...
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9answers
4k views

Perfect Squares!

A question was asked in a mental ability test yesterday. Write four distinct numbers with these properties: 1. Sum of each pair is a perfect square. 2. Sum of all four is also a perfect ...
12
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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 ...
8
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1answer
2k views

Can you pass through the ancient tomb? Find the correct interpretation for the symbols

You have been crossing this hot and wet place for weeks now, but when you enter the cool and mouldy ruin, you know in seconds it has been worth it. Nobody has ever been here ( - well nobody in last ...