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

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0
votes
1answer
48 views

Automatic searches for solutions to a recreational problem

I would like to examine the relationship of 5 numbers. 3,38,5,x set equal to .8 using abstract algebra. Yes I know (5/(38+3))*8 and (3/(38+5))*11 are close but I'm doing this all the time and I'd like ...
12
votes
5answers
881 views

Simplify : $( \sqrt 5 + \sqrt6 + \sqrt7)(− \sqrt5 + \sqrt6 + \sqrt7)(\sqrt5 − \sqrt6 + \sqrt7)(\sqrt5 + \sqrt6 − \sqrt7) $

The question is to simplify $( \sqrt 5 + \sqrt6 + \sqrt7)(− \sqrt5 + \sqrt6 + \sqrt7)(\sqrt5 − \sqrt6 + \sqrt7)(\sqrt5 + \sqrt6 − \sqrt7)$ without using a calculator . My friend has given me ...
20
votes
1answer
411 views

Does there exist a general solution of this 'Counting numbers' game?

A few days ago, a friend of mine taught me a number-game. It may be famous, but I haven't known it. I'm going to show it to you. Imagine that you have a kind of page-a-day calendar, and that you play ...
2
votes
2answers
464 views

distance between point and empty set

While playing with my little sister earlier we where inventing distances form earth to sun/stars/planets and who had the bigger distance wins. Now at some point she said "from earth to jesus" and ...
11
votes
3answers
1k views

What is the Probability that a Knight stays on chessboard after N hops?

Say a $8 \times 8$ chessboard as per picture. A position is represented here by co-ordinates $(x,y)$. A move is aslo considered as valid, where the Knight lands outside the chessboard [ For eg. ...
0
votes
2answers
110 views

Find n term of sequence

A sequence is given: $$1,10,11,100,101,110,111,1000,\dots,a_n,\dots$$ The question is: what is the value of $a_n$ for a given $n$? I have tried a lot of patterns but was not able to meet the ...
2
votes
2answers
205 views

What is the limit $( 1 + 1/\tan(n) )^{\tan(n)}$

What is the result of $\displaystyle \lim_{n\to \infty}\left(1+\frac{1}{\tan(n)}\right)^{\tan(n)}$ = ? The limit does not exist as stated by Adam Rubinson. Looks like the requested answer is e but ...
8
votes
7answers
246 views

Mathematical Games suitable for undergraduates

I am looking for mathematical games for an undergraduate `maths club' for interested students. I am thinking of things like topological tic-tac-toe and singularity chess. I have some funding for this ...
1
vote
1answer
360 views

Arithmetic progressions of perfect powers

Find the largest positive integer $n<100$, such that there exists an arithmetic progression of positive integers $a_1,a_2,...,a_n$ with the following properties. $1)$ All numbers ...
1
vote
1answer
99 views

Calculate the exact weekday of a given date.

I've seen questions about calculating the exact weekdays on a given day, such as the AMC few years ago asking for the weekday that Charles Dicken's birth. For example, yesterday's Sunday, August 4, ...
4
votes
4answers
4k views

Using + - * / operators and 4 4 4 4 digits find all formulas that would resolve to 1 2 3 4 5 6 7 8 9 10

I had a conversation with a colleague of mine and he brought up an interesting problem. Using the + - * / operators and four 4 4 4 4 digits, create an algorithm that will output all the formulas that ...
14
votes
4answers
464 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
1k 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
262 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
760 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
226 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 ...
62
votes
12answers
9k 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
178 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 ...
5
votes
1answer
182 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
62 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
301 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
98 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
623 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
378 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
471 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 ...
12
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
266 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
605 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 ...
0
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
151 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
512 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
155 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
110 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
766 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
112 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
263 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
14k 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
128 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
345 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
325 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 ...