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

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1
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1answer
50 views

Sum of largest two angles

All the inner angles of a 7 sided polygon are obtuse, their sizes in degrees being distinct integers divisible by 9. What is the sum (in degree) of the largest two angles?
-3
votes
2answers
1k views

Egg problem-Brain Teaser-Amazon Interview Question

A lady from the chicken farm gathers the eggs and brings it to sell it in the market. She sells the eggs but few eggs are left over. The 2nd day the left over eggs was doubled. Yet she sells the ...
3
votes
8answers
416 views

simple theorems that non-mathematicians can understand and appreciate.

For example, I stated this fact/theorem at a dinner to some friends and they were pretty impressed. Given any sequence of n integers, positive or negative, not necessarily all different, some ...
0
votes
1answer
63 views

Non-uniform scaling

I have 10 numbers $x_1, x_2, \dots, x_9, x_{10}$ which sum to a total of $1,000$. I want to scale these numbers so the total is equal to $10,000$, however I don't want them to scale exactly. I'm ...
10
votes
4answers
752 views

Recommended survey of mathematics [closed]

What do you see as the most explanatory and beautiful survey of mathematics book...For short is there a book like Feynman lectures but for math?I've looked at Elementary Mathematics from an Advanced ...
2
votes
3answers
838 views

There are 81 trees with {1,2,3,…81} apples on them respectively. Distribute among 9 people. Each get equal apples

It is clear. There are 81 apple trees. 1st tree has 1 apple, 2nd tree has 2 apples, 81st tree has 81 apples. Distribute the "trees" (not apples) among 9 people so everyone gets equal amount of apples. ...
0
votes
3answers
980 views

The largest number that cannot be made using a combination of $5$ and $11$?

Using just the numbers $5$ and $11$, what is the largest number that can not be made? An example of a feasible combination: $5 \cdot 20 - 11 \cdot 9 = 1$. An example of an unfeasible number is 13 ...
5
votes
2answers
309 views

A puzzle on game theory

Bob and Alice are playing a game. They will start with an integer $n$. Alice goes first, in each turn, a player can choose an integer between 1 and 13 and that number is to be subtracted from $n$. ...
5
votes
4answers
14k views

Find the pattern - puzzle

I have recently encountered a reasoning question that I have solved half , but I can't solve one part of it. Question : ...
10
votes
1answer
991 views

Maximally touching toruses

7 identical cylinders can mutually touch each other, if sufficiently long. For cylinders of different sizes, 8 can touch each other. What is the maximal number of mutually touching toruses? I ...
24
votes
4answers
1k views

Finding an invisible circle by drawing another line

A friend of mine taught me the following question. He said he found it in a book a few years ago. Though I've tried to solve it, I'm facing difficulty. Question: You know on a plane there is an ...
2
votes
2answers
221 views

Probabilities associated with negatively marked questions

First of all: not a native english speaker, and not a mathematician. Please explain as you would to your 10 years old son. I have 120 questions to answer True or False For each right answer, i ...
3
votes
3answers
621 views

number of points on two circles

(sorry I don't know how to add pictures) Two friends argue if larger circles have more points than smaller circles Friend number 1 (a well known argument) Say the circles are concentric. you cannot ...
0
votes
1answer
168 views

Discrete mathematics for someone from a non-mathematical background

I have been a software programmer for over six years and I'm from a non-mathematical background. Though I had some limited exposure to discrete mathematics in my college years it didn't leave any ...
1
vote
2answers
87 views

He would like to get and array where all entries are divisible by 2013.Then how many arrays are possible..?

Ramesh is given a $2013\times2013$ array of integers between $1$ and $2013$ both inclusive. He is allowed only $2$ operation. 1)Choose a row,subtract $1$ from each entry. 2)Choose a column ,add $1$ ...
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
872 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
409 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
455 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
108 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
235 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
353 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
96 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
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
996 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
257 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
729 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
223 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 ...
60
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
175 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
178 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
298 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
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
365 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
259 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
585 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 ...