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

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1
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1answer
143 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
505 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
152 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
737 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
254 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
13k 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
123 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
341 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
304 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
102 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
685 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
821 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
141 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
3k 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!
1
vote
2answers
70 views

Playing with a functional equation

I was playing with a functional equation and proved the result below: Let $f$ be such that $$f(f(z))=z$$ If $f^{-1}$ exists then $$f(z)=f^{-1}(z)$$ If $f'$ exists then as ...
2
votes
1answer
103 views

Number of days it took to climb the mountain (BdMO 2012 National Primary/Junior question)

From the Bangladesh Mathematical Olympiad 2012 National Secondary (Question 7, or ৭). When Tanvir climbed the Tajingdong mountain, on his way to the top he saw it was raining $11$ times. At ...
3
votes
1answer
221 views

Make $21$ out of $1,5,6,7$ (challenge).

Here is a small mathematical challenge. You have to use once and only once each of the four numbers $1,5,6,7$ in order to obtain, via the help of the usual operators ($+,-,/,*$ together with ...
8
votes
3answers
712 views

Smooth Pac-Man Curve?

Idle curiosity and a basic understanding of the last example here led me to this polar curve: $$r(\theta) = \exp\left(10\frac{|2\theta|-1-||2\theta|-1|}{|2\theta|}\right)\qquad\theta\in(-\pi,\pi]$$ ...
4
votes
2answers
160 views

Four integer numbers to express all integers from 1 to 40 [duplicate]

Let $a$, $b$, $c$, and $d$ four integers such that $0 <a <b <c <d$. We can get all integers from $1$ to $40$ by expressions containing or not only the numbers $a, b, c$ and $d$. In these ...
2
votes
5answers
529 views

Higher Dimenional Tic Tac Toe

Here we have a problem that seems very intuitive, but is hard to define mathematically. In Tic Tac Toe, we can find an equivalent of the game in any number of dimensions, it seems. The trick is to ...
0
votes
1answer
48 views

Adjust a range of given values. [duplicate]

If I have a number anywhere on the range 140 - 350 and I want to match it to the correlated range "0 - 360" what function can I run it through? i.e.:140 would go through the function and return 0.350 ...
36
votes
4answers
1k views

How does the divisibility graphs work?

I came across this graphic method for checking divisibility by $7$. $\hskip1.5in$ Write down a number $n$. Start at the small white node at the bottom of the graph. For each digit $d$ in ...
4
votes
4answers
243 views

Find the largest number having this property.

The $13$-digit number $1200549600848$ has the property that for any $1 \le n \le 13$, the number formed by the first $n$ digits of $1200549600848$ is divisible by $n$ (e.g. 1|2, 2|12, 3|120, 4|1200, ...
2
votes
2answers
221 views

Milk and Coffee will they ever finish

Let two glasses, numbered 1 and 2, contain an equal quantity of liquid, milk in glass 1 and coffee in glass 2. One does the following: Take one spoon of mixture from glass 1 and pour it into glass ...
3
votes
3answers
358 views

Solving $\;x+y+z =8 ; \;\;\sqrt{x^2+1}+\sqrt{y^2+4}+\sqrt{z^2+9}=10 $

Solve the problem \begin{cases}x+y+z =8 \\ \\ \sqrt{x^2+1}+\sqrt{y^2+4}+\sqrt{z^2+9}=10 \end{cases} with $(x,y,z) \in \mathbb R^3$ I have already solved it, but I'd like to see others creative ...
3
votes
2answers
295 views

Interesting Problems for NonMath Majors

Sometime in the upcoming future, I will be doing a presentation as a college alumni to a bunch of undergrads from an organization I was in college. I did a dual major in mathematics and computer ...
5
votes
2answers
246 views

Let $k \geq 3$; prove $2^k$ can be written as $(2m+1)^2+7(2n+1)^2$

Prove: If $k \geq 3$, then $2^k$ can be written as $(2m+1)^2+7(2n+1)^2$, where $k, m, n \in \mathbb{N}$.
9
votes
4answers
1k views

Proving that none of these elements 11, 111, 1111, 11111…can be a perfect square [duplicate]

How can i prove that no number in set S S = {11, 111, 1111, 11111...} Is a perfect square. I have absolutely no idea how to tackle this problem i tried rewriting it in powers of 10 but that didn't ...
1
vote
2answers
171 views

Grand Prix Race- Differential Equations [duplicate]

Driver A has boon leading archrival B for a while by a steady 3 miles. Only 2 miles from the finish, driver A ran out of gas and decelerated thereafter at ta rate proportional to the square of his ...
4
votes
1answer
578 views

How Many Clock Hand Positions Swap to a Valid Position?

My wording will not be exactly clear, but this is what I remember. Suppose you have a clock with minute and hour hands and you switch their places to form another correct time. How many such times ...
1
vote
3answers
138 views

Five digit re-write game

In the habit of factoring numbers, a notebook I bought had a five digit item number $77076$, which factors as $2^2 3^2 2141$, which may also be $9 \cdot 8564$, and in this form the count of digits is ...
2
votes
0answers
55 views

Symmetry between differentiation and integration [duplicate]

I want to make clear, that I am interested in the question: Why does integration need a bigger spectrum of functions than differentiation and not why integration is harder!!! as experience told me, ...
6
votes
1answer
212 views

cake cutting puzzle: why do finitely many cuts suffice?

Puzzle from http://www2.maths.bris.ac.uk/~majwm/compendium/cakeslice.php A piece of angle $x$ is cut from a cake, which is purple on top and yellow underneath, and turned upside down. Then another ...
2
votes
2answers
88 views

Expected number of pieces of a chessboard

If n squares are randomly removed from a $p \ \cdot \ q$ chessboard, what will be the expected number of pieces the chessboard is divided into? Can anybody please provide how can I approach the ...
3
votes
1answer
137 views

Minimum number of coconuts

Three friends namely $A$, $B$ and $C$ collected coconuts with the help of monkey and fell asleep. At night, $A$ woke up and decided to have his share. He divided coconuts into three shares, gave the ...
2
votes
5answers
377 views

When will two cars pass each other

There was a question in my math text book the other day that stated: $2$ cars each travelling at a constant velocity around a ring , complete exactly $4$ and $7$ rounds in one hour. If they start at ...
1
vote
1answer
174 views

Raise a number to the “y” power without using exponents.

This is kind of a spinoff on my question Divide by a number without dividing. Can anyone think of some clever ways to raise any given number to any given power without using an exponent anywhere in ...
-2
votes
4answers
779 views

Divide by a number without dividing.

Can anyone come up with a way to divide any given x by any given y without actually dividing? For example to add any given x to any given y without adding you would just do: $x-(-y)$ And to ...