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

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2
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1answer
261 views

Fifteen pennies lie on the table in the shape of a triangle

Fifteen pennies lie on the table in the shape of a triangle, with five pennies on each side. For some reason, the pennies are painted either black or white. Prove that there exist three pennies of ...
2
votes
1answer
111 views

Homotopy of a (non-spherical) cow.

I heard once that, from a topologist, that a cow and a doughnut ($\mathbb T^2$) are the same thing. It wasn't hard to believe that, since food enters by the snout and, well, goes out somewhere else. ...
3
votes
2answers
772 views

How to choose between an odd number of options with a fair coin

It is possible to choose between three equally desirable outcomes by tossing a fair coin as follows: Choose option 1 if the first head appears on an even toss Choose option 2 if the first tail ...
6
votes
1answer
101 views

Definite Integral that Evaluates to Teacher's Initials: TAA

My school's calculus teacher's birthday is in a couple of days, and our class decided to give him a surprise birthday card that has a definite integral which evaluates to his initials (TAA). So far ...
1
vote
1answer
41 views

Uniformed Distribution - Recap

I have divide the interval $[0,1]$ into $k$ equal sub-intervals, which I call classes, and generated $n$ observations from a uniform distribution. The number $X_{1}$ of the $n$ observations that fall ...
2
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2answers
236 views

Articles on matchstick puzzles

There are many ingenious puzzles involving matchsticks that are arranged as squares, rectangles or triangles, and can be moved under some restrictions (for a lot of examples see ...
5
votes
2answers
110 views

Can you incentivise competitors to handicap accurately, and also try to win?

A problem I ran into for real. A group of friends of widely differing abilities wants to hold a handicap cycling race, so that if everyone does about as well as expected, there would be a perfect dead ...
0
votes
1answer
3k views

How many triangle can be drawn with those points? [duplicate]

There are 7 points on the circumference of a circle.How many acute triangle can be drawn with those points. please help me to solve this problem.
1
vote
1answer
123 views

Next term in the sequence $1, 3, 33, 55, 565, 6567, 8767, …$?

My friend was asked this question at a job interview (it was nothing math related, so I assume it was more of a "let's see how you think" kind of question, not "how well can you identify series") and, ...
3
votes
0answers
206 views

Limits of infinite processes that terminate in finite time - checking my understanding?

I am a computer scientist by training, but have a fair amount of math background that I've picked up through classes, teaching, and general interest. A student of mine posed a question to me. I think ...
2
votes
2answers
195 views

A question about indeterminate forms

Are there any set of numbers into which any of the indeterminate forms we see in a calculus course, like 00, n/0, 1infinity, etc has an answer? I'm asking that because, thanks to the Net, I took ...
2
votes
0answers
261 views

Megaminx parity

I have an old 12-colored Megaminx that I put all new stickers on because the old ones were falling off. This Megaminx was in more of a state of disrepair than I originally thought, though, and when I ...
7
votes
1answer
118 views

Is it possible to have numbers that are to Hyperreal numbers what Hyperreals are to Reals numbers?

There are Hyperreal numbers that are smaller than any real number , also those that are larger than any real, they have properties analogous to those of Real numbers thanks to the Transfer principle ...
4
votes
0answers
82 views

Equality of nested radicals with different operations [duplicate]

I was playing around on Maple with some nested radicals and I notices that $$\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\cdots}}}}=\sqrt{2\sqrt{2\sqrt{2\sqrt{2\cdots}}}}=2$$ I thought my mind was playing tricks ...
1
vote
2answers
828 views

Math Riddles #10 - Car Meter Riddle

Today my car meter reads as 72927 kms. I notes that this is a palindrome. How many minimum kms I need to travel so my car meter find another palindrome?
1
vote
4answers
143 views

Jed does pushups every week day. On Monday he does 7. He doubles his average every day he works out. How many push ups does he do next Monday?

Jed does pushups every week day. On Monday he does $7.$ He doubles his average every day he works out. How many pushups does he do next Monday?
0
votes
1answer
147 views

number of ways to fill a 2D grid

We have a 2D grid with n rows and m columns, we can fill it with numbers between 1 and k (both inclusive). Only condition is that for each r such that 1<=r<=k ,no two rows must have exactly the ...
2
votes
2answers
111 views

how many ways to go from place a to place b through 9 squares

Please see the image. How many ways are there from M to N without passing through the sqaure more than once... I counted upto 6 ways...is it the right answer??
16
votes
4answers
566 views

Find all bijections $\,\,f:[0,1]\rightarrow[0,1],\,$ which satisfy $\,\,f\big(2x-f(x)\big)=x$.

A friend of mine gave me the following problem: Find all functions $f:[0,1]\to[0,1]$, which are one-to-one and onto and satisfy the following functional relation: $$ f\big(2x-f(x)\big)=x, \tag{1} $$ ...
1
vote
1answer
1k views

The 100 Coins Puzzle

There are 10 sets of 10 coins. You know how much the coins should weigh. You know all the coins in one set of ten are exactly a hundredth of an ounce off, making the entire set of ten coins a tenth of ...
1
vote
0answers
68 views

A Problem for the year with prime decomposition

I have noticed (and hope there are no errors) that: $$2013=3\times 11\times 61$$ $$2014=2\times 19\times 53$$ $$2015=5\times 13\times 31$$ while $2012$ and $2016$ are not the product of exactly ...
0
votes
1answer
100 views

What is the meaning of $(x^2+y^2)^n$? Is this an already known geometric object?

We all know that $x^2+y^2=r^2$ is a circle. What does $(x^2+y^2)^2$ signify? In general, what is $(x^2+y^2)^n$?
1
vote
1answer
239 views

Mismatching Results - Keno and Probability

In Keno, a player picks from 1 to 70 (at least in this version), 20 of these numbers are drawn, and the payouts are based on the number of matches. What I have tried to do is to check that the Swedish ...
0
votes
2answers
136 views

Sample paytable for slots

Could I get a sample paytable with at least $10$ combos for a $4$ reel slot machine with $6$ symbols on each reel with a house edge of $1 \%$? Pay table is the combinations in which you win for ...
2
votes
2answers
6k views

Determing the number of possible March Madness brackets

Is there a simple combinatorial explanation to derive the total number of march madness brackets? Would it be $2*(2^{16}*2^{8}*2^{4}*2^{2}*2)^{2}$ where the final squared takes into account both ...
0
votes
1answer
144 views

What are the simple Heesch-2 polyforms?

At the Tiling Database: There are 3, 20, 198, 1390 non-tiling polyominoes of order 7 to 10. There are 4, 37, 381, 2717 non-tiling polyhexes of order 6 to 9. There are 1, 0, 20, 103, 594, 1192, 6290 ...
3
votes
2answers
1k views

Making the water gallon brainteaser rigorous

This is a classic brainteaser. Suppose I have two water jugs of size 4 gallons and 7 gallons, and an infinite amount of water supply. I'm allowed to fill up a gallon completely, pour water into a a ...
8
votes
1answer
110 views

Range for values of cyclotomic polynomials, where $x$ is replaced by the golden ratio $0.61…$ ? And is it dense?

This is a recreational math question. I just played with the cyclotomic polynomials; and replacing $x$ by $1$,$-1$,$I$ gives some interesting patterns; setting $x=2$ seems to give some ...
2
votes
1answer
223 views

What's the least number of car parked?

In a car park, there are 2 white car for every 3 blue cars and for every 2 blue cars there are 5 silver cars. What is the least number of cars in the park? I am a bit confused about my ...
1
vote
2answers
239 views

A problem for math lovers to count the digits

Today a classmate of mine asked a question which is based on counting. Question. Find a positive integer which when multiplied up to $6$ times will give numbers having the same digits but rearranged ...
3
votes
1answer
185 views

Looking for a pattern in a math riddle

Looking to find a pattern but no idea how: $12\mathop{\square}21 = 86$, $13\mathop{\square}31 = 192$, $14\mathop{\square}58 = 389$, $14\mathop{\square}94 = \ ?$
1
vote
1answer
104 views

Probability puzzle - Two people drawing marbles… what is the probability one will be the first to get a certain color

One of my relatives had a probability question that they asked me that was a little puzzling... What do you think? Can anyone explain how to do a problem like this? A container has six yellow ...
2
votes
1answer
139 views

Are there mathematical blogs/websites which publish “pop-math”?

Are there mathematical blogs/websites which publish "pop-math" (that is, simple and nice articles on interesting topics aimed at ...
0
votes
2answers
141 views

I have a button…(story problem)

Tom has a job. He is a button pusher. He works for 8 hours per day. his job at work is simply to push a button. He has some freedoms and some limitations. When he arrives to work each day he has 5 ...
1
vote
0answers
77 views

How can $1 + 2 + 3 + … = -\frac{1}{12}$? [duplicate]

Recently there's been a lot of buzz created by this video http://www.youtube.com/watch?v=w-I6XTVZXww which states and goes on to prove $$1 + 2 + 3 + ... = -\frac{1}{12} $$ I know that the above ...
0
votes
1answer
53 views

What is the easiest and fastest way to produce a uniformly distributed random number between 0 and 9 off the cuff?

Let’s assume, you are in a rush and you need a random number: What is the best way to produce a high-quality, uniformly distributed random integer number between 0 and 9, ideally using only mental ...
0
votes
1answer
146 views

Card game question

In a game where we have a normal 52 card deck. Two cards are delt out at a time, if both are red, then I keep the two cards. If both are black, you keep the two cards. If its one of each, then it gets ...
3
votes
3answers
3k views

Magic Trick to Read your Mind

I am a student in High School. My math professor made a magic trick the other day in my class and he read our minds. I knew a similar trick which was based on mathematics, that's why I am asking here. ...
0
votes
1answer
48 views

Sorting $N$-ary Gray codes into a plane/grid

Is there a formal algorithm to arrange a set of "numbers" on a grid/plane such that each adjacent set differs from the other by only one value. Something similar to the Grey code but further extended ...
0
votes
3answers
124 views

How many ways can you ascend a stairway of any number of steps?

I wrote out by hand every way from 1 to 6 steps and came up with the formula $f(x) = 2^{x-2}$. Is that correct? I then tried to solve the problem recursively but could not. So I wanted to know if my ...
10
votes
2answers
898 views

$12345679$ and friends

We can see that in the decimal system each of $12345679\times k$ $(k\in\mathbb N, k\lt 81, k\ \text{is coprime to $9$})$ (note! not $123456789$) has every number from $0$ to $9$ except one number as ...
0
votes
1answer
149 views

Playing around with ${\int\frac{dx}{x^2-2x}}$

Found the above integral in the old posts and figured I would play around with it using double substitution and integration of partial derivatives. So here goes. $$\int \frac {dx}{x^2-2x}$$ $$= ...
0
votes
1answer
407 views

Striking off a digit from each of the numbers written in seven rows, while preserving arithmetical operations

Problem Strike off any digit from each number in seven rows (need not be at same place) and combine the same operations with 3 digit numbers to get the same addition. After this strike off another ...
1
vote
1answer
3k views

Sum of cubes of the digits of a number equal to to the number

I have a number, I don't know how large or small, but if I cube the digits of the number and sum them, the sum is equal to the number itself. In other words, $$\sum_{k=1}^n{a_k^3}=\sum_{k=1}^{n}{a_k ...
4
votes
2answers
808 views

What is the parity of permutation in the 15 puzzle?

You might know the 15 puzzle: $\hskip1.4in$ Concerning the solvability, Wiki says: The invariant is the parity of the permutation of all 16 squares plus the parity of the taxicab distance ...
0
votes
1answer
290 views

Relative Percentage vs Percentage Change

If I have a number say "500" and I say that it spiked 4 times (400%) of the original value i.e. "2,000". Does that make sense mathematically and grammatically because I'm talking about relative ...
0
votes
2answers
79 views

Define S as a set of primes such that if a, b are in S, ab+4 is in S. Show that S must be empty.

Define $S$ as a set of primes such that $(a \in S) \land (b \in S) \implies (ab + 4) \in S$ [$a$ and $b$ can be the same number]. Show that $S$ must be empty. A hint is given ... "work modulo 7." ...
5
votes
3answers
4k views

Are there more even numbers than odd numbers?

Very simple 'yes-or-no' question, but I can't find the answer anywhere. My gut feeling says the number of odd and even numbers are equal but I managed to write up something that contradicts my ...
0
votes
1answer
32 views

Given $a, b, c, d, m \in\mathbb{Z}$such that $5\mid (am^3 + bm^2 + cm + d)$, prove that there exists integer $n$ such that…

Given $a, b, c, d, m$ in $\mathbb{Z}$ such that $5|(am^3 + bm^2 + cm + d)$ and $5 \not| d$ , prove that there exists an integer $n$ such that $5\mid(dn^3 + cn^2 + bn + a)$ I've spent about two hours ...
4
votes
0answers
188 views

Measuring how change in input variables contributes to output in non linear equation.

How do we measure how a variable contributes to an output as its value increases, and how it relates to other input variables? Let's say we're playing a video game, where you can buy items to augment ...