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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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9 votes
1 answer
3k views

Two-Move Chess Game

Consider a standard game of chess. We make the following modification: on a turn, if a player makes a move which neither captures a piece nor puts their opponent’s king in check, then they may make a ...
godlification's user avatar
0 votes
8 answers
633 views

How to sell at the buying price and still have something in hand? [closed]

A farmer walked into the cattle market and found the price is fixed at "5 for 2 coins", either buy or sell. He thought a little and then bought cattle of 250 cows for 100 coins (250/5 * 2). ...
Shahram Alemzadeh's user avatar
14 votes
1 answer
741 views

$\pi$ = 13, $\sqrt{2}$ = 7, $e$ =?

From The Escape Room Advent Calendar: Puzzle book for adults I know the answer to this puzzle. I cannot for the life of me figure out why it is what it is.
jla's user avatar
  • 263
20 votes
8 answers
3k views

Which parent should you start playing against?

Let $k < n$, $k$ even, $n$ odd. Mary is to play $n$ chess games against her parents, alternating between her father and mother. To receive her allowance she must win $k$ games in a row. Given the ...
Simd's user avatar
  • 7,845
10 votes
4 answers
396 views

Irregularly Deposited Compound Interest

Suppose you have a very peculiar bank account that obeys the following rules: The account pays 10% interest per year, generated continuously. Interest from the account does not compound automatically;...
Tim C's user avatar
  • 2,544
0 votes
1 answer
85 views

Minimum function optimization puzzle #4: Using negative numbers?

Previous puzzle Take this puzzle of mine that I created around a week ago: Take these 3 functions: $f(x):=x+8,g(x):=x^2-3,h(x):=\sqrt x$ Starting from $x=0$,$$\color{black}{\text{How many times will ...
CrSb0001's user avatar
  • 2,241
2 votes
1 answer
268 views

Nimber mnemonic combinatorial puzzle

Please see my previous question for more background. The following represents an unfolded version of PG(3,2) with 1 as the center point: Given that each number must be an end point of a line which ...
stargirl's user avatar
12 votes
1 answer
968 views

Relatively prime numbers

Can you fill in the circles with numbers such that: Each pair of circles connected by one line contains relatively prime numbers Each pair of circles connected by two lines do not contain relatively ...
godlification's user avatar
21 votes
5 answers
3k views

Mishustin's circle problem

This problem was given to high school students by the Russian prime minister Mishustin. We have a circle. We are given some point on the circle and its diameter, as shown below. We are given a ...
Dmitry Kamenetsky's user avatar
2 votes
1 answer
231 views

Nimber Mnemonics

Note I originally tried to ask a variation of this question on math.stack; however 1 commenter pointed out that math.stack is not a puzzle site, which made me think maybe the fine folks of puzzling ...
stargirl's user avatar
9 votes
3 answers
1k views

Rearrange words to make a sentence

The following puzzle is from the October 1961 issue of the Eureka journal (published by The Cambridge University Mathematical Society): Rearrange the order of the following so as to make a true ...
Will Octagon Gibson's user avatar
2 votes
1 answer
189 views

Pursuit-evasion game [closed]

A criminal has been spotted along a straight single-filed road of length $L$ at position $P$, measured from the left endpoint of the road! Two police officers arrive to the road at positions $A$ and $...
Kevin's user avatar
  • 39
3 votes
1 answer
249 views

Longest subsequences and shortest longest ones

This challenge is about permutations of the integers 1 to 30 with longest increasing subsequence length 3. An important part of the definition is that a subsequence is not necessarily contiguous or ...
Simd's user avatar
  • 7,845
-1 votes
2 answers
136 views

Create a permutation with longest increasing subsequence length 3

Create a permutation of the integers 1 to 30 with longest increasing subsequence length 3. An important part of the definition is that a subsequence is not necessarily contiguous or unique.
Simd's user avatar
  • 7,845
0 votes
1 answer
184 views

Find the wrong number in the given series

I found this question in an Indian Highschool Reasoning Olympiad. I tried looking for any relation using powers of 2 but failed.
Darshit Sharma's user avatar
-2 votes
1 answer
159 views

Progressive matrix: Matrices

This is a progressive matrix problem that I created myself and I can confirm that there is only one unique solution. It may look complex at first, but is pretty easy when you figure out what to do. \...
CrSb0001's user avatar
  • 2,241
6 votes
6 answers
6k views

'SILVER' -> ‘LESIRU' and 'GOLDEN' -> 'LEGOND', so 'NATURE' -> what?

I found this problem in an Indian Highschool Reasoning Olympiad. (image) If 'SILVER' is coded as 'LESIRU' and 'GOLDEN' is coded as 'LEGOND', then in the same code language how 'NATURE' will be coded ...
Darshit Sharma's user avatar
2 votes
1 answer
168 views

Kind of a Number Pattern

I found this problem in a highschool Reasoning olympiad in India.
Darshit Sharma's user avatar
5 votes
1 answer
805 views

Minimum number of turns

You have 64 identical-looking boxes numbered from 1 to 64, each weighing a distinct amount. On a turn, you can tell your friend two numbers between 1 and 64, and she will tell you which of the ...
quantrader23's user avatar
1 vote
1 answer
230 views

In a certain code 'NATIONAL' is written as 'JUBOKZMN'. How is 'ELECTION' written in that code?

In a certain code 'NATIONAL' is written as 'JUBOKZMN'. How is 'ELECTION' written in that code? (A) FMFDSHNM (B) DFMFMNHS (C) DMFMFHNS (D) MFDFHSMN I really tried many basic methods using positional ...
Darshit Sharma's user avatar
4 votes
1 answer
363 views

The Monty Hall loot box

Everyone sufficiently competent in probability knows that in The Monty Hall problem as most commonly presented, switching doors wins you the car $\frac23$ of the time. I have come up with this ...
Parcly Taxel's user avatar
  • 7,678
1 vote
2 answers
322 views

Equality-breaking function

There's a function that satisfies the following: $f(2) = 1, f(2^2) = 2, f(-3^3) = 3$ $f^n(x) = 3(n-1) + f(x)$ Where $f^n$ means $f$ composed with itself $n$ times. Lastly, $f$ is not equality ...
user110391's user avatar
0 votes
2 answers
135 views

Minimum function optimization puzzle #3: 3 functions

Previous puzzle Take this puzzle of mine I created recently: Let $f(x)=x+1$, $g(x)=x^2-1$, $h(x)=2x-4$. Starting with $x=0$ and applying these functions as needed, what is the minimum amount of times ...
CrSb0001's user avatar
  • 2,241
0 votes
3 answers
164 views

Counting puzzle #1: Function combinations

Not in conjunction with my function optimization puzzles, also sorry for the extremely difficult discrete mathematics puzzle So as you may or may not know, I have recently uploaded 2 function ...
CrSb0001's user avatar
  • 2,241
0 votes
2 answers
109 views

Minimum function optimization puzzle #2

Previous puzzle Take this puzzle of mine I created about an hour ago Take two functions, $f(x):=x^2$ and $g(x):=x-3$. Starting from $x=0$ and applying these functions as needed, what is the minimum ...
CrSb0001's user avatar
  • 2,241
1 vote
1 answer
176 views

Is my solution to a mathematics puzzle I created the most efficient solution there is to it?

Here's a puzzle of mine that I created around 2 hours ago: Let $f(x):=x^2$ and $g(x):=x-4$. Starting with x=0, what is the least amount of times you need to apply the functions $f$ and $g$ so that at ...
CrSb0001's user avatar
  • 2,241
4 votes
6 answers
5k views

What is the probability that your life will have lasted for 100 years once you die?

You are in a world where exactly 90% of all people live for exactly 3 years, and exactly 10% of all people live for exactly 100 years. Aside from what I mention here there is no information that can ...
Anders Gustafson's user avatar
-2 votes
1 answer
313 views

Create numbers from 1-100 using 1846

Create all numbers $1$ to $100$ using equations made up of $1,4,6,8$. Rules: Use all four digits exactly once Allowed operations: $+,\,-,\,\times,\,\div,\,!$ (factorial), exponentiation ($a^b$), ...
sonia ahuja's user avatar
6 votes
1 answer
775 views

Find the numbers (can’t use digits other than 1)

Can you find two numbers composed only of ones which give the same result by addition and multiplication? Of course 1 and 11 are very near, but they will not quite do, because added they make 12, and ...
Will Octagon Gibson's user avatar
8 votes
1 answer
375 views

Shuffled binary numbers version 2

Here are 0 to 15 in binary: 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 I have shuffled and concatenated them to obtain the following strings:...
Dmitry Kamenetsky's user avatar
7 votes
4 answers
1k views

Prove that in an n*(n+1) table filled with integers, we can always cross out some columns and make the sum of the integers in each row, even

The boxes of an n * (n+1) table ( n rows and n+1 columns) are filled with integers. Prove that one can cross out zero or several columns ( not all of them ) so that after this operation, the sum of ...
Hemant Agarwal's user avatar
2 votes
3 answers
404 views

Button multi arm bandit problem

Let's say you have the following buttons to press, labeled a - j, that would earn you the following amounts of money: a: \$6 b: \$9 c: \$15 d: \$26 e: \$45 f: \$78 g: \$136 h: \$416 i: \$728 j: \$...
user55665484375's user avatar
7 votes
2 answers
752 views

Shuffled binary numbers

Here are 0 to 15 in binary: 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 I have shuffled and concatenated them to obtain this string: ...
Dmitry Kamenetsky's user avatar
-3 votes
2 answers
207 views

Improving Judgement pill problem [closed]

Lets say there are 10 different pills that improve or impair judgement each assigned a rating (1-10) of increasing or impairing your judgement (1 stupid, 5 normal, 10 super smart) You currently know ...
user55665484375's user avatar
4 votes
3 answers
1k views

an esoteric matchbox

Seeing a vast repository of matchstick puzzles, Professor Moriarty determined to create one of his own. Behold, his greatest crime yet, the best and worst matches puzzle to ever grace this earth with ...
MWQOJYNWQA's user avatar
0 votes
2 answers
411 views

A 4x4 sudoku shouldn't be that hard, right? Right?

Note: this is not in conjunction with my Minesweeper puzzles Got this idea from one of Cracking the Cryptic's videos, I don't remember which one though. This exact puzzle is still overall unique. ...
CrSb0001's user avatar
  • 2,241
17 votes
3 answers
1k views

Put infinitely many equilateral triangles of equal size on the plane

...such that There's no overlapping No more such triangles can be added without overlapping. Let $r$ be, on average, the ratio of the area covered by triangles with respect to the area which is not. ...
Eric's user avatar
  • 6,498
0 votes
1 answer
63 views

Construction of non-rhombus but still paralellogram non-square-non-rectangle non-kite via Pythagorean triplet

Is it possible to construct a non-rhombus but parallelogram and quadrilateral non-square, Non-rectangle by putting four 3-4-5 (Pythagorean triplet) triangles together and making the 90 degree angle ...
user avatar
-7 votes
1 answer
129 views

What is the number after 19? 1,4,8,13,19

It's a question on the application for my it certification school
 XAmberDawnX's user avatar
4 votes
1 answer
284 views

10000 rounded to the nearest integer is 22

10000 rounded to the nearest integer is 22, 20000 rounded to the nearest integer is 2101, 100000 rounded to the nearest integer is 212, and 200000 rounded to the nearest integer is 21010. What is ...
mathlander's user avatar
  • 1,241
0 votes
0 answers
124 views

2048: how many sets of moves have I made? [duplicate]

Transcription of board (score 324): 2 2 32 4 8 16 2 32 4 4 8 2 I made moves in the pattern of: right up left down right up left down. How many times have I done this set? (1 set=right up left ...
ChickinBorgur's user avatar
3 votes
3 answers
382 views

5x5 grid with a special colouring

Can you paint the cells of a 5x5 grid in 5 colours such that for each cell its colour and the colour of its orthogonal (horizontal and vertical) neighbours are all different?
Dmitry Kamenetsky's user avatar
27 votes
1 answer
3k views

2048: How many turns did I survive?

Here's my most recent 2048 game: Clicking on the image takes you to the 2048 site. Transcription of board (final score 59612): 2 4 8 4 8 32 64 16 4096 2 512 256 2 8 1024 8 How many turns ...
mathlander's user avatar
  • 1,241
27 votes
8 answers
4k views

How many dogs of Oxford are there?

The dogs of Oxford, I declare: Numbered one third of a square. If one quarter left to roam, Just a cube would stay at home. What is the smallest possible number of dogs in Oxford? This is a ...
ApexPolenta's user avatar
  • 2,722
5 votes
0 answers
255 views

Longest Fibonacci word

Fibonacci words are defined as $F_0 = a, F_1 = b, F_{n+2} = F_nF_{n+1}$ where $a, b$ are letters. How can you find the longest Fibonacci sub-word in a given string? Try to solve it in linear time ($O(...
popcorn's user avatar
  • 151
-5 votes
1 answer
77 views

Using 8 6 4 2 = 6 in that order using only x - +

One more question.. Using 8 6 4 2 = 6 in that order using only x - + 👍🏾
Karen Chappell's user avatar
-4 votes
1 answer
226 views

Using 8 6 4 2, how do you get to 30

8 6 4 2 =30 in that order using only + - X
Karen Chappell's user avatar
3 votes
3 answers
431 views

The infinite bag of billiards balls

The following trio of puzzles comes from http://skepticsplay.blogspot.com/ My question is: What is the solution to variation 2? The original author of these puzzles described them as being abstract. ...
Will Octagon Gibson's user avatar
-1 votes
2 answers
137 views

Let's make a huge number with only tiny numbers (pt3)

Previous huge out of tiny puzzle by TerriblyDrawn Using only four ones, four twos, and five fives (1, 1, 1, 1, 2, 2, 2, 2, 5, 5, 5, 5, 5), can you make the complex number$$51+5i\sqrt5$$You can use ...
CrSb0001's user avatar
  • 2,241
1 vote
5 answers
374 views

Let’s make a huge number with only tiny numbers (pt2)

Using only three 1s and two 2s (i.e. 1,1,1,2,2), can you generate the smallest 3-digit prime number, 101? You can use all mathematical operators you know, such as floor function, factorial, powers/...
TerriblyDrawn's user avatar

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