Questions tagged [mathematics]

A puzzle related to mathematical facts and objects, whose solution needs mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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24 votes
3 answers
9k views

A general solution to the decanting problem? (aka jug-pouring, water-pouring)

Take a look at these two questions: - A Set of Water Jug Challenges - Pouring problem Now I'm asking for a generalised solution to that problem. I define the problem as follows: You are required ...
  • 8,722
34 votes
2 answers
3k views

Determine the algorithm

So I was given this puzzle quite some time ago and just thought it would make a nice addition to this site: Your task is to determine the method how the result is determined from the given number. A ...
  • 2,376
23 votes
2 answers
12k views

Coin weighing problem

You are given ten stacks of golden coins, each stack consisting of ten coins and a digital scale with arbitrary precision. You know that all stacks of coins are made from gold, weighing 10 grams per ...
  • 2,376
21 votes
5 answers
7k views

N logicians wearing hats of N colors

N logicians are wearing hats which can be of N different colors (each hat has one color; there can be multiple hats with the same color). Each logician can see the colors of all hats except his own. ...
121 votes
7 answers
28k views

100 Prisoners' Names in Boxes

Names in Boxes The names of 100 prisoners are placed in 100 wooden boxes, one name to a box, and the boxes are lined up on a table in a room. One by one, the prisoners are led into the room; each may ...
  • 1,937
82 votes
15 answers
98k views

A camel transporting bananas

A somewhat well-known puzzle is described as such: You have a pile of 3,000 bananas. You wish to transport them to a place 1,000 miles away on the back of a camel; however, the camel can only carry ...
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11 votes
4 answers
12k views

N balls and a scale

The question of twelve balls and a scale is probably the best-known example of the "find the ball of a different weight" problem. But does it generalize? Is there a general way to find a weighing ...
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93 votes
7 answers
23k views

Why does this solution guarantee that the prince knocks on the right door to find the princess?

I found this puzzle online: On the top floor of a castle lives a princess. The floor has 17 bedrooms arranged in a row. Each bedroom has doors connecting to the adjoining bedrooms as well as to the ...
  • 2,375
39 votes
3 answers
6k views

Pirates and gold coins

A group of N pirates has come by a chest containing 200 gold coins. Their rules require that the coins be distributed by the following approach. The pirates are ranked from fiercest to meekest and ...
24 votes
6 answers
80k 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 ...
  • 564
34 votes
8 answers
6k views

Dinosaur egg drop

Archeologists discover two dinosaur eggs, and you are given the chance to test the durability of these eggs (bad move on their part). Suppose that these eggs will absorb a specific amount of force ...
  • 2,086
130 votes
8 answers
23k 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 ...
  • 2,373
47 votes
4 answers
15k views

I don't know the two numbers... but now I do

Two perfect logicians, Summer and Proctor, are told that integers 𝑥 and 𝑦 have been chosen such that 1 < 𝑥 < 𝑦 and 𝑥 + 𝑦 < 100. Summer is given the value 𝑥 + 𝑦 and Proctor is given ...
  • 2,324
13 votes
4 answers
2k views

Nerds, Jocks, and Lockers

Here's an oldie but goodie from The Daily WTF; I paraphrase to avoid copyright issues: A middle school math teacher, who also happened to be the P.E. coach, made the following deal with the non-...
  • 474
10 votes
6 answers
716 views

Find the value of $\bigstar$: Puzzle 1 - Evaluation

This puzzle replaces all numbers with other symbols. Your job, as the title suggests, is to find what number fits in the place of $\bigstar$. All symbols abide to the following rules: Each symbol ...
  • 659
23 votes
4 answers
4k 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 ...
  • 699
124 votes
13 answers
23k views

Paying the Troll toll

You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made. Between your house and her house, you have to cross 7 ...
48 votes
11 answers
287k views

6, the magic number

Here's a fun (albeit difficult) one: Make these equations true using arithmetic operations: ...
  • 2,376
14 votes
6 answers
3k views

Use 2 0 1 and 8 to make 67

Use $2$ $0$ $1 $ and $8$ to make the number $67$ RULES You must use all 4 digits. Only the digits 2, 0, 1, and 8 can be used. You can make multi-digit numbers out of the numbers. Examples: 20, 82, ...
  • 1,873
6 votes
3 answers
432 views

Find the value of $\bigstar$: Puzzle 2 - Switch-a-roo

This puzzle replaces all numbers with other symbols. Your job, as the title suggests, is to find what number fits in the place of $\bigstar$. All symbols abide to the following rules: Each symbol ...
  • 659
27 votes
3 answers
8k 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)...
  • 2,086
11 votes
6 answers
15k views

1 Fake Coin among N Amount of coins

You are given $N$ coins which consists of only $1$ fake coin. You also have a sensitive old-fashioned Pan Balance Scale. You are asked to find the fake coin in totally 5 times weighing on the Pan ...
  • 28.9k
22 votes
3 answers
18k views

Write twenty-four from four numbers

Write 24 using the four numbers 1, 3, 4, 6 and basic arithmetic. Explanations: The given are numbers, not digits, so you can't group them using decimal notation. For example, you can't create the ...
  • 15.9k
12 votes
1 answer
352 views

Follow the path of relation through the grid #1

There is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-right corner of the grid. Each square can ...
  • 2,252
8 votes
4 answers
358 views

Find the value of $\bigstar$: Puzzle 3 - Substitution

This puzzle replaces all numbers with other symbols. Your job, as the title suggests, is to find what number fits in the place of $\bigstar$. All symbols abide by the following rules: Each symbol ...
  • 659
12 votes
3 answers
938 views

Input/Output Problem #1

The basis for this problem is that you did to make an optimal pattern so that all inputted sequences will be "accepted" if they fit the rules of the problem and "rejected" if they break any of them. ...
7 votes
1 answer
256 views

Follow the path of relation through the grid #2

There is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-right corner of the grid. Each square can ...
  • 2,252
6 votes
2 answers
241 views

Find the value of $\bigstar$: Puzzle 4 - In Between

This puzzle replaces all numbers with other symbols. Your job, as the title suggests, is to find what number fits in the place of $\bigstar$. All symbols abide to the following rules: Each symbol ...
  • 659
6 votes
1 answer
212 views

Follow the path of relation through the grid #3

There is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-right corner of the grid. Each square can ...
  • 2,252
3 votes
2 answers
2k views

Make numbers 93 using the digits 2, 0, 1, 8

I have a 1 to 100 building challenge with 2, 0, 1, 8, all made but 93 is not made. I need your help! This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 8. Rules: Use all ...
  • 161
139 votes
8 answers
42k 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?
47 votes
10 answers
185k views

1 2 3 4 5 6 7 8 9 = 100

The sequence of numbers $1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9$ has the property that you can insert mathematical operators in between the numbers from $1$ to $9$ and make the expression evaluate to 100. For ...
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22 votes
4 answers
6k 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 ...
  • 17.9k
21 votes
3 answers
6k views

N pirates steal their share of bananas to the benefit of a monkey

The following is a type of logic / math puzzle I've yet to see on this site. I feel it belongs because the kernel of this problem can be reworked into other puzzles. $N$ pirates find themselves ...
  • 9,012
33 votes
18 answers
11k views

Use 2, 0, 1 and 8 to make 109

Assemble a formula using the numbers $2$, $0$, $1$, and $8$ in any order that equals 109. You may use the operations $x + y$, $x - y$, $x \times y$, $x \div y$, $x!$, $\sqrt{x}$, $\sqrt[\leftroot{-2}\...
  • 4,136
32 votes
3 answers
6k views

Maximum time for ants to fall off stick

Suppose there are $n$ ants on a stick which has length 1. At any time, the ants may be facing left or right, the initial directions of the ants are arbitrary. Each ant can be modeled as a point in the ...
  • 3,743
19 votes
4 answers
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 ...
  • 1,253
23 votes
4 answers
7k 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 ...
  • 9,012
15 votes
2 answers
1k 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 ...
  • 4,932
10 votes
1 answer
3k 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 ...
  • 14.2k
6 votes
7 answers
8k 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. ...
  • 199
4 votes
2 answers
317 views

Find the value of $\bigstar$: Puzzle 5 - Every little Symbol

This puzzle replaces all numbers (and operations) with other symbols. Your job, as the title suggests, is to find what value fits in the place of $\bigstar$. All symbols abide to the following rules:...
  • 659
57 votes
8 answers
5k views

Find a straight tunnel

There is a circular area with radius 1 km. And there is a tunnel, which is just under the surface, but invisible - unless you dig. It is known that the tunnel goes under the area (at least touches it ...
  • 15.9k
15 votes
1 answer
1k views

One beer too many

You're standing outside your apartment building after a late night out, with perhaps one beer too many, and you realize you have completely forgotten the code to get in. Luckily, you're a mathematical ...
  • 696
15 votes
3 answers
97k views

If you choose an answer to this question at random, what is the chance you will be correct? [duplicate]

If you choose an answer to this question at random, what is the chance you will be correct? A) 25% B) 50% C) 60% D) 25% (source: twimg.com)
16 votes
1 answer
4k 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 ...
  • 265
-2 votes
7 answers
19k views

2x2 row and column equations

Rules: No paper or notes, but a calculator is accepted. Post the exact time min wise of how long it took. And obviously give the answer.
  • 569
4 votes
1 answer
2k views

Missing number in this sequence?

I heard this puzzle in a quiz I participated in: 10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, ?, 100, 121, 10000 What is the missing number? (You don't need to do any big calculations, and you don't ...
3 votes
3 answers
419 views

Find the value of $\bigstar$: Puzzle 6 - Enclosed Operations

This puzzle replaces all numbers (and operations) with other symbols. Your job, as the title suggests, is to find what value fits in the place of $\bigstar$. All symbols abide to the following rules:...
  • 659
3 votes
1 answer
157 views

Follow the path of relation through the grid #4

There is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-right corner of the grid. Each square can ...
  • 2,252

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