Puzzles, curiosities, brain teasers and other mathematics done "just for fun".

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0
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0answers
105 views

Upside down bell shaped graph moving with respect to $x$ axis

Basically, I wanted to create a "loser" graph. Along the $x$ axis we'd have time and along the $y$ axis is how much of a loser someone is. I want the graph to be an upside down bell shaped graph ...
0
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3answers
124 views

Given $n+1\mid2\sum_{k=1}^{n}{a_k}$, find $a_k$.

Let $m$ be a positive integer. There are only 2 finite sequences of positive integers like $a_1,a_2,...,a_m$ such that $$(\forall n \leq m)\left(n+1\mid2\sum_{k=1}^{n}{a_k}, \quad a_n\in [1,m],\quad ...
3
votes
2answers
288 views

Conjecture I came up with

For each number translated into binary $0$, $1$, $10$, $11$, $100$, $101$, $110$, $111$, $1000$, ... find a number where, when you take the length of the binary number, the binary number and the ...
3
votes
1answer
761 views

Correct Path To Castle Riddle [duplicate]

I'm working on the following riddle that I found to be kind of interesting, but I can't figure it out. The problem is as follows: A prince visits an island inhabited by two tribes. Members of one ...
1
vote
1answer
61 views

What is the max single day score on jeopardy?

So, I was trying to figure out what the max score on jeopardy is for a single day. what I did was account for the daily doubles at the very end with the lowest value category, (to save on the 1000's), ...
2
votes
1answer
98 views

What is the difference in chance, based on foreknowledge of the resolution?

I'm working to understand the differences between Odds, Probability and Chance. I've come up with a hypothetical situation to show where I'm having a bit of an issue. Chad shuffles a standard deck ...
5
votes
3answers
247 views

What is the most mathematically sound way to define the “damage per second” for a weapon?

Consider a weapon firing shots every $f^{-1}$ seconds (i.e. $f$ is the weapon's fire rate). Each shot deals $n$ damage to is target. Consider another weapon firing every $3f^{-1}$ second, but dealing ...
0
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1answer
73 views

Problem with probability

If we choose randomly an infinite, countable set of disks in $\mathbb R^2$, what is the probability that intersection of every pair of disks from the set is an empty set? EDIT: Because the problem in ...
81
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1answer
3k views

$4494410$ and friends

The number $4494410$ has the property that when converted to base $16$ it is $44944A_{16}$, then if the $A$ is expanded to $10$ in the string we get back the original number. ...
6
votes
2answers
505 views

How to Construct orthogonal circles?

Let $C_{1}$ be a circle of unit radius. Let A and B be two points inside $C_{1}$. Now I want to construct another circle $C_{2}$ such that A and B lie on $C_{2}$ and $C_{2}$ is orthogonal to $C_{1}$ ...
1
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0answers
44 views

maximising the frequency of mode.

I have 4 numbers 5,5,3,1. Now I have the number 5, which I can distribute in any manner to ...
0
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1answer
90 views

Compute Birthdate From Age

I have an interesting problem. I want to compute a birthdate (Month Date, Year) from a given age. I understand that subtracting the given age from the current date will supply the year of birth, but ...
2
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0answers
234 views

Dates and times with no repeated digits?

I have a digital clock that shows the date and time like this: $$ \mathsf{YYYY-(M)M-(D)D\qquad (H)H:MM \; [:SS]} $$ That is, the seconds display is optional, and if the month or day or hour is ...
6
votes
2answers
1k views

Sailors, monkey and coconuts

Five sailors and a monkey were shipwrecked on a deserted island, and they spent the first day gathering coconuts for food, piled them all up together and went to bed. But when they were all asleep one ...
1
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3answers
128 views

Help on French Math Education Paper

I am looking for very basic (probably I should say very elementary) papers in french designed for elementary school teachers and elementary school educators. I would appreciate if someone can provide ...
2
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0answers
123 views

A system of linear equations in integer squares - solvable?

I consider this more a "recreational math" problem, possibly lacking a solution (because it stems from the question of "magic square of squares") or simply intractable with reasonable effort. ...
11
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3answers
554 views

Arc sums for a circle of $k$ positive integers whose total sum is $n$

This problem got me thinking about the following more general scenario: Suppose you have $k$ positive integers with total sum $n$, and you arrange them in a circle. Given such an arrangement, you ...
6
votes
2answers
284 views

Concise naming-scheme for polyominoes

There is a neat naming scheme for pentominoes based on letters they resemble. Is there a generalized naming scheme for polyominoes? If there isn't a canonical one, can you think of a good one? ...
6
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1answer
4k views

Expected number of calls for bingo win

Before I begin, I did a search through math.stackexchange and came across two previous attempts to get people to solve probability problems involving bingo. Neither produced a response. So what ...
0
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1answer
207 views

Buddhabrot Sewing machine [closed]

The Buddhabrot fractal traces the orbits of the points outside the Mandelbrot set. What design considerations need to be taken into account to create a computerised sewing machine that traces out ...
9
votes
1answer
253 views

Is the number of alternating primes infinite?

I'm not sure if the recreational-mathematics tag is appropriate, but this problem came up during a practice Putnam seminar so maybe? The problem: Say that a positive integer is alternating if ...
5
votes
3answers
1k views

Cyclic sums — How do you use them?

Can someone give me an example of how cyclic sums are used? I don't really understand how they're used in problem-solving. For example, $$\sum_{a,b,c}a^2$$ Any help would be appreciated, and I'm not ...
11
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2answers
1k views

Is there a collection of alternative mathematical notation? (Semi-soft Question)

I'm interested in alternative systems of notation for mathematics. I've often heard how mathematical notation is illogical, inconsistent, filled with grandfather clauses that serve no purpose, and ...
2
votes
1answer
77 views

Question on pathological sine function

Some years ago I came across what was defined as "pathological" function defined as: $$ f(x)=\sum_{k=1}^\infty \frac{1}{k^2}\cdot \sin\left(k!\cdot x\right) $$ It was mentioned (in an article I ...
15
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5answers
1k views

Is high school contest math useful after high school?

I've been prepping for a lot of high school math competitions this year, and I was just wondering if all the math I learn would actually mean something in college. There is a chance that all of it ...
5
votes
4answers
155 views

Example of a question that would seem not to have enough information for an answer

Looking for an example of a question that would seem not to have sufficient information for an answer, or a question that the solution would not require (or maybe even maybe hindered ) by the extra ...
9
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0answers
169 views

Number of circles in configuration

Consider the $n^2$ lattice points $(i, j)$, where $1 \leq i, j \leq n$. Let the number of circles that pass through at least 3 points of this set be $C(n)$. What is a good way to count this? Is there ...
1
vote
2answers
469 views

How many ways to write one million as a product of three integers?

In how many ways can the number 1;000;000 (one million) be written as the product of three positive integers $a, b, c,$ where $a \le b \le c$? (A) 139 (B) 196 (C) 219 (D) 784 (E) None of the ...
1
vote
1answer
109 views

Discrete Maths question

Show that $S=\{1,3,4,5,9\}$ is a difference set for $\Bbb Z_{11}$. Identify the design produced from $S$ by the sets of the form $S+i$, $i \in\Bbb Z_{11}$.
12
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1answer
207 views

Request for a proof of the following continued-fraction identity

I have been poring over many texts about continued fractions, but none of them seem to be helping me to prove the following beautiful continued-fraction identity (I am nowhere close): $$ ...
2
votes
2answers
4k views

How can you construct as many intersections as possible with n lines?

If you have $n$ lines, it seems to be obvious that you can have at most $\frac{n^2-n}{2}$ intersections: $n = 1$: Obviously you need two lines to intersect, so the maximum number of intersections is ...
1
vote
1answer
530 views

Puzzle of $N$ men around a table

This was asked to me by a friend. $N$ men sit around a circular table. Man 1 has a sword with him and he kills the Man 2, Man 3 picks up this sword and kills the next person i.e. Man 4. Thus the man ...
0
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1answer
219 views

How to solve this algorithmic puzzle?

For fixed integers $T\geq G>1$, we say a list $[a_1, a_2,\cdots, a_n]$ is normal if every consecutive sublist $[a_i, a_{i+1}, \cdots a_{i+T-1}]$ of length $T$ has less than $G$ maximal elements. ...
4
votes
1answer
155 views

Prove that all combinators must fulfill A x = x for some x, given that M x = x x and composability of any two combinators

I'm working through Raymond Smullyan's "To Mock a Mockingbird" and I'm stuck on the first problem in the combinatory logic section. I'd appreciate hints, but no spoilers please. The problem is ...
12
votes
1answer
276 views

The number of prime years in a lifetime

$2013$ is not a prime: $3 \times 11 \times 61$. I was born in a prime year, and if I live as expected according to the statistics for U.S. males, I will just reach another prime year, $2027$. That ...
7
votes
3answers
161 views

Trouble simplifying a tough equation

I'm having trouble simplifying the following equation. I've tried grouping terms in different ways, but it's not looking any more joyful. Can someone please help with its resolution? Hopefully by ...
5
votes
1answer
363 views

How is tessellation defined in Mathematics?

Hi. I am a GCSE student and I am interested in Maths. I read few books on maths and learned some mathematical analysis. I know of convergent series but I would like to know how identical sets(not ...
2
votes
3answers
133 views

Pat the Mathemamagician Part 2

Sal the Magician asks you to pick any five cards from a standard deck. You do so, and then hand them to Sal’s assistant Pat. Then you pick one of the five cards, and Pat puts it back into the deck, ...
3
votes
0answers
138 views

Is there a way to determine how many solution does “ The hundred Fowls problems” have looking at the coefficients?

I was looking at the different versions of the hundred fowls problems. I came across the problem posed by Chinese mathematicians posed in 5th century,and then Indians in 9th, 10th centuries. Alcuin of ...
6
votes
3answers
322 views

Palindrome of numbers from 1-n

A palindrome is a number or word that is the same when read forward and backward, for example, “176671” and “civic.” Can the number obtained by writing the numbers from 1 to n in order (n > 1) be a ...
1
vote
1answer
48 views

How to get range of 1 to 10 by index?

I have a collection of lessons divided by levels Each level has 10 chapters. ...
83
votes
3answers
8k views

Topology: The Board Game

Edit: I've drawn up some different rules, a map and some cards for playing an actual version of the game. They're available at my personal website with a Creative Commons Attribution 4.0 license. ...
1
vote
3answers
619 views

$5n+1$, $3n-1$ problem, smallest repeating cycle and Collatz conjecture

Among the Collatz conjecture we have other "similar" problems that are solved and have repeating cycles. $5n+1$ has the repeating cycle $13, 66, 33, 166, 83, 416, 208, 104, 52, 26$, with a length of ...
5
votes
3answers
250 views

What is the value of D here?

Number $S$ is obtained by squaring the sum of digits of a two digit number $D$. If the difference between $S$ and $D$ is $27$, then the two digit number $D$ is? My thoughts: Let the two digit number ...
1
vote
2answers
251 views

$N \equiv 3 (\textrm{mod } 4)$ and Collatz conjecture

Can the Collatz conjecture also be interpreted as behaviour, transformation of number of form $N\equiv 3(\textrm{mod }4)$ to the form of $N\equiv 1(\textrm{mod }4)$ Because integers of the form ...
2
votes
1answer
251 views

Dissection of a chess board into 4 congruent pieces

Consider a standard $8\times 8$ chessboard where a pawn is placed on each of the squares $d1,d2,d3,d4$ . Dissect the board into $4$ congruent pieces (reflections are allowed) such that each piece ...
3
votes
2answers
64 views

Calculating the most efficient number of group payment transactions required

If you have a group of people who purchase items together and split the costs (not always evenly). How can you calculate the most efficient number of transactions required to settle outstanding debt. ...
0
votes
4answers
418 views

A logic puzzle from TES: Arena

Its nice when games have riddles hidden in them. While playing TES:Arena, I came across an unusual logical puzzle: There are 3 cells. If Cell 3 holds worthless brass, Cell 2 holds the gold key. If ...
18
votes
1answer
413 views

Mathematical Quine

I have recently discovered that I can create letters and any shape I want by hiding parts of curves by making them complex. To generalise if I want $x>a$ then I multiply my function by ...
6
votes
2answers
1k views

Useless math that become useful

I'm writing an article on Lychrel numbers and some people pointed out that this is completely useless. My idea is to amend my article with some theories that seemed useless when they are created but ...