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

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14
votes
4answers
463 views

Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$

Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$ Doesn't this thing approaches 0 at the end? why does it approaches 1?
0
votes
2answers
93 views

function with restrictions in finding solutions

Please help... How to prove the following functional equation, which has no solution. $A + B + C + (A + B)C - 2 = 0$ has no solution, where $A = f(x)$, $B = g(x)$ and $C = h(x)$. Here $A, B$ and $C$ ...
13
votes
5answers
950 views

Areas of math that can be “gamified”?

My old high school math teacher has started up a math club recently. It's become quite popular (to my pleasant surprise), and I've been looking for ways to contribute. To that end I've been looking to ...
3
votes
2answers
256 views

Finding Grandma's Car - a word problem

This word problem came up in a lunchtime discussion with coworkers. None of us are professional mathematicians or teachers of math, and we weren't sure how to get the answer. The word problem goes ...
16
votes
1answer
714 views

How many different shapes can I make with this toy?

I have the following toy, perhaps some of you have seen it before. It consists of a bunch of cubes with an elastic string in the middle. You can bend it into different shapes like this: Or this: ...
0
votes
3answers
220 views

Find 7 digit prime numbers with this property;

When you subtract the sum of the squares of the digits of the number from the original number it gives you another prime number squared.
3
votes
1answer
71 views

Partition the following graph into 4 parts

Partition the following graph into $4$ parts, each with the same shape-size, and each with one circle in it. $$\begin{array}{cc} 1& 1& 1& 1& 1& 1\\ 0 &0 &1 &1 &1 ...
58
votes
12answers
8k views

Can the golden ratio accurately be expressed in terms of e and $\pi$

I was playing around with numbers when I noticed that $\sqrt e$ was very somewhat close to $\phi$ And so, I took it upon myself to try to find a way to express the golden ratio in terms of the ...
3
votes
2answers
172 views

Avoid more than one duplicate opponent

OK, I'm not sure if I can explain this: I have 12 players I want that each player play 3 times Each game is of 3 vs 3 players In each game each player plays with 2 different team members (no ...
4
votes
1answer
175 views

Board $7\times 7$ problem

An aid in this problem: On a board of $7 \times 7$ each box is painted red or blue so that any square on the board has at least two neighboring boxes blue. determine as little blue boxes that can be ...
-1
votes
1answer
61 views

Is it possible to merge two teams of final rankings with one team having 7 members, and the second team having 24 members?

Is it possible to merge two teams of final rankings with one team having 7 members, and the second team having 24 members? Is there a formula to provide one total overall ranking between the groups? ...
0
votes
1answer
57 views

Derive a formula to solve a specific task

I have a specific problem. I have 8 different variables a, b, c, d, e, f, g, h. Each of these variables has a score out of 5, where 1 is bad and 5 is good. So a max score of 45 and a min of 0. Of ...
6
votes
5answers
295 views

pandigital rational approximations to the golden ratio and the base of the natural logarithm

Steven Stadnicki suggested in a comment that I post the following as a question. The golden ration $\phi$ is given by $$\phi = \frac{1+\sqrt{5}}{2} \approx 1.618033988.$$ A rational approximation is ...
2
votes
2answers
96 views

Building a circle containing a specific number of points on a plane

Given a 2-dimensional plane containing $n$ random points, prove that it's always possible to build a circle containing exactly $k$ points; where $n\gg k$. A friend told me this problem and the ...
18
votes
5answers
620 views

Is $3 \ge 1$ or is it just $3 > 1$?

Well, probably this might seem a really simple question (and it might be so too!), but off late me and my friends have been debating quite hard over this question. Is $3 \ge 1$ or is it just $3 ...
0
votes
0answers
130 views

Annoying the entire world

Okay, so I had this conversation with a friend: [7時41分48秒] Me: INTERESTING CALCULATION TIME (y)` [7時41分55秒] Me: if everybody who is annoyed [7時42分01秒] Friend: lol [7時42分01秒] Me: ...
4
votes
2answers
353 views

Logic puzzle, generic form

This logic puzzle has stumped me for some time now: You are in a dark room with a deck of cards in front of you. 30 cards are face down and the rest are face up. How can you separate the cards into ...
15
votes
4answers
469 views

$\square\square\times\square =\square\square\square =\square\times\square\square\,\,\,$ fill blanks with distinct numbers from$\{1,2,3,4,5,6,7,8,9\}$

Fill in the blanks of: $$\square \;\square \times \square = \square \; \square \;\square =\square \times \square \;\square $$ With distinct numbers from the set $\{1,2,3,4,5,6,7,8,9\}$. I was ...
11
votes
1answer
2k views

What is the most efficient numerical base system?

I remember reading somewhere that base $e$ is the most "efficient" base system because of its ratio of possible characters to number length. For example, binary is "inefficient" because each ...
0
votes
1answer
92 views

what is the new order of the digits here ? Both the numbers $144$ and $441$ consists of the same digits?

$12^2=144$ Here in, $144$ the hundreds digit is 1. The $1$ has travelled to the units place below in $21$ as well as $441$. $21^2=441$ What can be said of the $4's$ ?
6
votes
2answers
257 views

$20$ hats problem [duplicate]

I've seen this tricky problem, where $20$ prisoners are told that the next day they will be lined up, and a red or black hat will be place on each persons head. The prisoners will have to guess the ...
0
votes
0answers
62 views

Calculating earnings after few taxes

I have a scenario like this: there is an EVENT which is time based and has some kind of 'tax' on it. PARTICIPANTS can join and leave an EVENT any time while EVENT is running. each PARTICIPANT can ...
7
votes
2answers
570 views

Dissection puzzle for area 49 to area 50

49 and 50 are close, as are 288 and 289. That allows a grid illusion. If cut out of wood, perhaps with coloring on the border as an "assistance", the pieces could be dumped out of the tray, flipping ...
-1
votes
3answers
1k views

Hands of a clock forming certain angles

How many times to the hands of a clock form a 60 degree angle between noon and midnight on the same day? Firstly im not sure weather they require the second hand to be included. And secondly (excuse ...
1
vote
1answer
139 views

Functions to pick up orderly the elements on the SW-NE half diagonals in a half matrix (lower triangular part)

I wish to write a program that does the following, and I need some math help figuring out a simple formula to pick up elements in the lower triangular part of a matrix. Consider the lower bottom-left ...
1
vote
0answers
98 views

gcd finding method

An integer $d$ is a $\gcd$ of two non-zero integers $a$ and $b$, if $d$ divides $a$ & $d$ divides $b$ '$c$ divides $a$ & $c$ divides $b$' implies '$c$ divides $d$' for any integer $c$. If ...
3
votes
1answer
498 views

Throw a die three times, and get maximum number of different sums.

The IBM Ponder This problem for July 2013 throws an 8 sided die 3 times, and can get 120 possible different positive integer sums. If all the faces have positive integer sides, what is the lowest ...
10
votes
1answer
150 views

Is there any curriculum based on recreational mathematics?

I'm a high school physics teacher. Next year, I'll be teaching mathematics for middle school students so I was wondering if there's a curriculum based on recreational mathematics which not only ...
1
vote
1answer
98 views

ideas for finding the roots of an annoying polynomial

This is an easy question, in a way, but I've been trying to solve it for the better part of the day and I'm getting nowhere. Specifically, I have the equation $$ f(x) := a - 2\sqrt{bx} - ...
3
votes
1answer
109 views

Problem about a process with bins of balls

A friend of mine give me this problem for fun: Given $\frac {n(n+1)}{2}$ balls, first we divide arbitrarily these balls in baskets, after that we make another basket with one ball of each basket e do ...
1
vote
0answers
35 views

Are there infinitely many emirps? [duplicate]

An emirp is a prime number such that when its decimal digits are reversed, one obtains a different prime number. Are there infinitely many ermips? It is apparently open whether there are infinitely ...
0
votes
2answers
683 views

Formula for sequences

Can you guess a general generating rule for these 7 sequences ? 2 3 4 2 3 4 3 4 4 2 3 4 3 5 4 5 4 5 6 2 3 4 3 5 4 6 5 4 6 5 6 5 6 6 2 3 4 3 5 6 4 7 5 4 6 5 7 6 5 7 6 7 6 7 7 2 3 4 3 5 6 4 7 5 8 ...
3
votes
2answers
110 views

Does this process always terminate?

Consider the following "game". Take two natural numbers $n \leq m$ and let $S=n+m$ and $P=nm$. Take two logicians A and B, and tell A the value of $S$ and B the value of $P$. Now, A and B alternate ...
3
votes
1answer
85 views

$k$ cards summing to $n$

This was a problem posted about probability involving Fibonacci numbers that I thought was really interesting so I decided to repost a portion of it regarding a general closed formula. The problem ...
4
votes
4answers
246 views

If Sam's age is twice the age Kelly was two years ago, Sam's age in four years will be how many times Kelly's age now?

If Sam's age is twice the age Kelly was two years ago, Sam's age in four years will be how many times Kelly's age now? (A) .5 (B) 1 (C) 1.5 (D) 2 (E) 4 So say at -2 years Sam's age is 12 and ...
0
votes
1answer
12k views

Finding functions for an angle whose terminal side passes through x,y

How would I "Find the six trigonometric functions for the angle theta whose terminal side passes through the point (-8,-5)"?. I learned this material over 2 years ago and since then have forgotten. I ...
2
votes
2answers
120 views

Name for grid system

Is there a name for a type of grid you might find in Battleship? Where coordinates don't relate to points on a grid but rather the squares themselves?
24
votes
1answer
337 views

The final number after $999$ operations.

I wanted to know, let the numbers $1,\frac12,\frac13,\dots,\frac1{1000}$ be written on a blackboard. One may delete two arbitrary numbers $a$ and $b$ and write $a+b+ab$ instead. After $999$ such ...
7
votes
1answer
295 views

Word problem (food for thought)

I thought of this question today as I was coming home from work in my car (probably because of my parents' anniversary). This problem assumes the parents of everyone in the world got married and ...
3
votes
2answers
101 views

How do you solve this word problem?

The river is flowing from point A to B at a rate of 15 miles per hour. A boat moves on still water at 45 miles per hour. If it takes David 1 hour and 15 minutes to ride the boat on the river from A to ...
3
votes
1answer
89 views

An asymmetric die game

Suppose there is a prisoner who is being held by a gambling-addicted warden. The warden offers a compromise to the prisoner - if the prisoner can win a certain game of chance, the warden will let them ...
7
votes
2answers
3k views

Is there any mathematical theory behind sudoku?

In particular I would like to know: is it possible to say if a sudoku is solvable only having the initial scheme? If yes, what are the condition for which it is solvable? Given the initial scheme of ...
6
votes
2answers
1k views

How many triangles in picture

How many triangles in this picture:
26
votes
20answers
2k views

Interesting Math for 3-graders

I'm supposed to give a 30 minutes math lecture tomorrow at my 3-grade daughter's class. Can you give me some ideas of mathemathical puzzles, riddles, facts etc. that would interest kids at this age? ...
22
votes
3answers
1k views

A gambler with the devil's luck?

A gambler with $1$ dollar intends to make repeated bets of $1$ dollar until he wins $20$ dollars or is ruined. Probabilities of win/loss are $p$ and $(1-p)$, and each bet brings a gain/loss of $1$ ...
6
votes
1answer
664 views

Proof of Closed Form Formula to convert a binary number to it's Gray code

The Gray code for a binary number $x$ is given by $$ x \oplus \lfloor x/2 \rfloor $$ How can this formula be mathematically proved ?
30
votes
1answer
2k views

Minesweeper - Chance of one-click win

I'd like to know if it's possible to calculate the odds of winning a game of Minesweeper (on easy difficulty) in a single click. This page documents a bug that occurs if you do so, and they calculate ...
2
votes
2answers
804 views

Area puzzle in colored triangle [duplicate]

I have tried to figure out by calculating the area but I got same results for these, so where is gone the hole?
2
votes
1answer
134 views

kaleidoscopic effect on a triangle

Let $\triangle ABC$ and straightlines $r$, $s$, and $t$. Considering the set of all mirror images of that triangle across $r$, $s$, and $t$ and its successive images of images across the same ...
8
votes
2answers
4k views

What's the difference between Complex infinity and undefined?

Can somebody please expand upon the specific meaning of these two similar mathematical ideas and provide usage examples of each one? Thank you!