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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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 ...
- 8,792
40
votes
3
answers
4k
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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 ...
- 2,436
23
votes
2
answers
12k
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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 ...
- 2,436
23
votes
5
answers
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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. ...
123
votes
7
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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 ...
- 1,987
85
votes
16
answers
205k
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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 ...
user88
12
votes
4
answers
13k
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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 ...
user88
94
votes
7
answers
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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 ...
- 2,393
10
votes
6
answers
891
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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 ...
- 761
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 ...
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34
votes
8
answers
6k
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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 ...
- 2,106
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votes
6
answers
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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 ...
- 574
24
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 ...
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133
votes
8
answers
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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 ...
- 2,433
48
votes
4
answers
16k
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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 ...
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13
votes
4
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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-...
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6
votes
3
answers
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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 ...
- 761
127
votes
12
answers
29k
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 ...
- 2,204
47
votes
11
answers
288k
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6, the magic number
Here's a fun (albeit difficult) one:
Make these equations true using arithmetic operations:
...
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13
votes
6
answers
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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, ...
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8
votes
4
answers
422
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 ...
- 761
28
votes
3
answers
9k
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)...
- 2,106
25
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3
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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 ...
- 16.1k
23
votes
4
answers
3k
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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 ...
- 1,313
12
votes
1
answer
364
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 ...
- 2,296
11
votes
6
answers
16k
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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 ...
- 30.2k
4
votes
2
answers
426
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:...
- 761
33
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 ...
- 5,632
16
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2
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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 ...
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12
votes
3
answers
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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.
...
- 905
7
votes
1
answer
269
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 ...
- 2,296
6
votes
1
answer
221
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 ...
- 2,296
6
votes
7
answers
8k
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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. ...
- 199
6
votes
2
answers
289
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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 ...
- 761
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
3
votes
3
answers
451
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:...
- 761
142
votes
8
answers
45k
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?
- 1,906
47
votes
10
answers
187k
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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 ...
anon
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}\...
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votes
4
answers
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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 ...
- 18.1k
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4
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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 ...
- 9,072
21
votes
3
answers
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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 ...
- 9,072
16
votes
4
answers
6k
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No broken eggs puzzle
Three men went to buy eggs from an eggs seller:
The first ordered half of the seller's stock plus half of an egg.
The second ordered half of what's left in the stock plus half of an egg.
The third ...
- 2,564
11
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 ...
- 14.4k
57
votes
8
answers
6k
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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 ...
- 16.1k
16
votes
1
answer
4k
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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 ...
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votes
3
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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)
- 293
15
votes
1
answer
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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
4
votes
1
answer
2k
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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 ...
- 116k
4
votes
2
answers
398
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 ...
- 761