# 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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### Add as few plus signs as possible to make equation true

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you! ...
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### How to define "edge orientation" on a pyraminx?

I have a question about the pyraminx twisty puzzle. I've included a bit of background to make sure we're all using the same words. (background) To the initiated, a pyraminx is a triangular-looking ...
119 views

### Minimum number of swaps

This puzzle is related to this math question. Consider $4$ lists of integers: $(0,0,0,0,0,0,0,0)$, $(1,1,1,1,1,1,1,1)$, $(2,2,2,2,2,2,2,2)$, $(2,2,2,2,2,2,2,2)$ where order does not matter. We want to ...
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### What are the next 3 terms: 19, 43, 59, ...?

What are the next 3 terms in the following finite sequence? 19, 43, 59, 23, 79, 83, 109, 463, 569, 263, ?, ?, ?
360 views

### Does this random sequence contain the number 1?

Randomly choose a number from 1 to 3 and call it $a_1$; Randomly choose a number from 1 to 3$a_1$ and call it $a_2$; Randomly choose a number from 1 to 3$a_2$ and call it $a_3$; $\cdots$ Repeat this ...
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### 125034 v2.2 / 2023-12-21 Q1(m=6)

I am developing a game that generates puzzles every day. It's my opinion that these puzzles are like Einstein's Riddle in 1D. Two weeks later, it will generate the following puzzle for players looking ...
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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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### 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 ...
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 ...
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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 ...
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 ...
171 views

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 $... 3 votes 1 answer 233 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 ... -1 votes 2 answers 127 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. 0 votes 1 answer 153 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. -2 votes 1 answer 138 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. \... 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 ... 2 votes 1 answer 155 views ### Kind of a Number Pattern I found this problem in a highschool Reasoning olympiad in India. 5 votes 1 answer 774 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 ... 1 vote 1 answer 198 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 ... 4 votes 1 answer 319 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$of the time. I have come up with this ... 1 vote 2 answers 306 views ### Equality-breaking function There's a function that satisfies the following:$f(2) = 1, f(2^2) = 2, f(-3^3) = 3f^n(x) = 3(n-1) + f(x)$Where$f^n$means$f$composed with itself$n$times. Lastly,$f$is not equality ... 0 votes 2 answers 134 views ### Minimum function optimization puzzle #3: 3 functions Previous puzzle Take this puzzle of mine I created recently: Let$f(x)=x+1$,$g(x)=x^2-1$,$h(x)=2x-4$. Starting with$x=0$and applying these functions as needed, what is the minimum amount of times ... 0 votes 3 answers 142 views ### Counting puzzle #1: Function combinations Not in conjunction with my function optimization puzzles, also sorry for the extremely difficult discrete mathematics puzzle So as you may or may not know, I have recently uploaded 2 function ... 0 votes 2 answers 108 views ### Minimum function optimization puzzle #2 Previous puzzle Take this puzzle of mine I created about an hour ago Take two functions,$f(x):=x^2$and$g(x):=x-3$. Starting from$x=0$and applying these functions as needed, what is the minimum ... 1 vote 1 answer 167 views ### Is my solution to a mathematics puzzle I created the most efficient solution there is to it? Here's a puzzle of mine that I created around 2 hours ago: Let$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 ... 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 ... -3 votes 1 answer 278 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 ($a^b$), ... 6 votes 1 answer 766 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 ... 8 votes 1 answer 361 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:... 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 ... 2 votes 3 answers 395 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: \$... 6 votes 2 answers 735 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: ... -3 votes 2 answers 204 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 ... 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 ... 0 votes 2 answers 389 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. ... 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. ... 