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

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2answers
46 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 ...
1
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0answers
49 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
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1answer
72 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 ...
3
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0answers
61 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 ...
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2answers
107 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?
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4answers
105 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?
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0answers
40 views

Waiting Time For Computer Cluster

There are $n$ computers. Computer users stay on their computers for a certain amount of time, $t$, throughout the day. Computer users come and go. How long will I have to wait, min/max, for a computer ...
0
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1answer
53 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
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2answers
49 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??
1
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1answer
127 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 ...
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0answers
55 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 3 ...
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1answer
89 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 $(x^2+y^2)^n$?
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1answer
50 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 ...
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2answers
56 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 ...
1
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1answer
748 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
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1answer
51 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 ...
2
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2answers
161 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
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1answer
85 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
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1answer
51 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 ...
0
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2answers
190 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 $N$ times will give numbers having the same digits but differently ...
3
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1answer
132 views

Looking for a pattern in a math riddle

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

Finding the amount of beads they had at first

Maria and Farida had 250 beads altogether. After Maria used 18 beads to make a bracelet and Farida gave away 2/5 of her beads they have the same number of beads left. How many beads did Maria have at ...
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1answer
60 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
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1answer
86 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 ...
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2answers
102 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 ...
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0answers
50 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 ...
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1answer
48 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
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0answers
79 views

How many melodies are there?

Clearly if we assume only 12 chromatic notes to the scale, not all of which sound good next to each other, a melody of length $N$ chooses from less than $12^N$ potential melodies. Allowing melodies to ...
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1answer
108 views

Game theory 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 ...
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4answers
84 views

What is Answer Of This Aptitude Question? [closed]

Friends This is my Aptitude Question. ...
3
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3answers
365 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. ...
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1answer
26 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 ...
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3answers
59 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 ...
9
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2answers
518 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
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1answer
146 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. $$\int \frac {dx}{x^2-2x}$$ $$= ...
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0answers
86 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 ...
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2answers
68 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 ...
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1answer
45 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 ...
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2answers
54 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." ...
2
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2answers
266 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 ...
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1answer
93 views

A Nim game variant: Odd number [closed]

Consider the variant of Nim where the allowed moves are the removals of an odd number of stones from a heap. Who's the winner and what is the winning strategy in normal play (player unable to move ...
0
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1answer
24 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
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0answers
138 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 ...
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1answer
102 views

Rubik's Cube Question

I tried doing a little bit of googling about this, but I am not able to find a decent answer. Let a configuration of a face be a choice of color for each of the 9 squares on that face of the cube. Is ...
4
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1answer
70 views

How to draw by hand mathematical figures?

Does there exist a kind of tutorial in order to learn to draw by hand complicated surfaces? For example, the two-sheeted covering of the Klein bottle (drawn by Jean-Pierre Petit in Le retournement non ...
4
votes
1answer
75 views

999 coins in 3-by-3 piles

999 coins are organized in a 9 piles in a $3\times 3$ grid. There number of coins in each column is the same (333). We are allowed to take the 3 piles in a single row, but only if we manage to ...
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1answer
67 views

Please help me solve this problem [closed]

Every month, a girl gets an allowance. Assume one year ago she had no money, and so saved each month's allowance over the past year. Then, she spends $\frac{1}{2}$ of her money on clothes; then ...
6
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0answers
211 views

Prime factor of $2 \uparrow \uparrow 4 + 3\uparrow \uparrow 4$

I checked the prime factors of $$2 \uparrow \uparrow 4 + 3\uparrow \uparrow 4 = 2^{2^{2^2}} + 3^{3^{3^3}}$$ with trial division and found non below $8*10^9$ Nevertheless, the given number has still ...
4
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2answers
39 views

Property With Specific Properties

I am thinking of making a game (for the mathematicians that study numbers) in which players try to construct a set with certain properties. Which properties satisfy the following: Formally, every ...
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1answer
71 views

what is the most sided sturdy regular n-polygon that can be made with lego?

Was puzzeling with this question: What is the most sided regular n-polygon that can be made with lego? It has to be sturdy (the polygon should stay in shape when pushed around) made with the normal ...