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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Nondivisibility by 11 puzzle
Source: MacPOW Problem of the Week 1240
Take this math puzzle:
The number 545 has the curious property that upon replacing the digit in any single position by an arbitrary digit (from 0 to 9; it can ...
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4
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How to solve 1 2 3 4 5 = 5 4 3 2 1 (insert five pluses to make it equal)? A thorough solution needed
I consider it an amazing though very challenging puzzle:
1 2 3 4 5 = 5 4 3 2 1
One must insert exactly five pluses (i.e. five addition signs) somewhere between those ten displayed figures in such way ...
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Zeroes in natural numbers up to a googol
How many times does the digit $0$ occur in the list of numbers from $1$ to $10^{100}$, inclusive?
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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 ...
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Obtain all digits using only 0
Combine digits you have into numbers and perform mathematical operations with them to get the rest of the digits. You may use all mathematical operations.
You start with 0.
Example:
You have digits 0,...
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A Sierpiński Carpet ratio
This math problem popped into my head and I wanted to share it with you:
We have the Sierpiński carpet, which is a fractal built like this:
Draw a square.
Divide it into 9 equal subsquares arranged ...
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Let's break PolynumCrypt
Introducing a super secure function to crypt your sensitive data - PolynumCrypt!
Say you wanted to crypt the string $\text{super}$, with a key of $6$.
Get the ASCII values of the string, ...
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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).
...
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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 ...
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$\pi$ = 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.
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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;...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 $...
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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 ...
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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 ...
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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.
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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 ...
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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.
\...
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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 ...
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'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 ...
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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.
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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 ...
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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 ...
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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 ...
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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 ...
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Cooperative guessing game: no incorrect guesses
There are 15 players who will play a cooperative game. They begin by closing their eyes. A referee will place either a black hat or a white hat (chosen by fair coin flip) on each player's head. The ...
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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 ...
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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 ...
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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 ...
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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 ...
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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: \$...
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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 ...
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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 ...
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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 ($a^b$), ...
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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 ...
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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:...
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What are the hidden digits in this long division puzzle?
The following problem was given in the Eureka journal (April 1978/University of Cambridge). This problem can be solved by hand without computers. There is a unique solution. The phrase, "exact ...
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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 ...
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Measure the rod
You are given three meter scales A, B, and C are shown in picture given below. The scales are however, quite unique in their properties as they have different numbers of division per meter. You are ...
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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.
...
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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:
...
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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 ...
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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.
...
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Was Humpty Dumpty right?
Raymond Smullyan's What is the Name of This Book? contains a puzzle which I'll paraphrase here:
Of the identical twins Tweedledum and Tweedledee, one of them lies on Mondays, Tuesdays and Wednesdays ...
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