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

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5
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1answer
83 views

Hockey Classics at Matheletics '13

I'm trying to solve a challenge from Matheletics '13: Micheal Nobbs is organizing a training camp for identifying new talents in Indian Hockey. The camp witnessed a total of ($3K+1$) players. Each of ...
4
votes
1answer
276 views

BINGO Probability: Controlling average game duration

I wandered over here from StackOverflow and my understanding of advanced mathematics is limited, so bear with me... A standard, BINGO game card has 24 numbers arranged in a 5x5 format. The center of ...
6
votes
3answers
164 views

What went wrong?

Intrigued by this question, one-dimensional inverse square laws, I started to try to find an answer and came up with what follows. However, I calculated the derivatives to double check myself, and ...
6
votes
1answer
124 views

Integer coefficient polynomial - values as powers of 2

Does there exist a polynomial f with integer coefficients such that $f(0) , f(1) ... f(n) $ are all distinct powers of 2 ? I have no clue about how should i start thinking about this problem but ...
2
votes
1answer
73 views

Functions which satisfy $\mathrm{f}(wz) =w\,\mathrm{f}(z)+z\,\mathrm{f}(w)$

Let $\mathrm{f}$ be a complex-valued function with the following property: $$\mathrm{f}(wz) =w\,\mathrm{f}(z)+z\,\mathrm{f}(w) $$ for all $w,z \in \mathbb C$. Necessary conditions are that ...
73
votes
12answers
7k views

Logic puzzle: Which octopus is telling the truth?

King Octopus has servants with six, seven, or eight legs. The servants with seven legs always lie, but the servants with either six or eight legs always tell the truth. One day, four servants met. ...
0
votes
3answers
892 views

How do you find the altitude in a pyramid? (SAT math question)

The pyramid shown above has altitude h and a square base of side m. The four edges that meet at V, the vertex of the pyramid, each have length e. If e = m, what is the value of h in terms of m? A) ...
9
votes
0answers
150 views

Are there known pairs of simple numbers equal to huge precision, but not equal strictly?

Are there known pairs of numbers $a$ and $b$, which at first look at them seemed likely to be equal, and after checking up to $10^n$ decimal places appeared to agree, but suddenly for some $n$ they ...
1
vote
1answer
139 views

Primes created by “n + digital-root(n)” sequences

I've looked at the sequences created by repeatedly adding the digital root of a number to the number until it becomes prime. This is the pseudo-code for the program I've used:   n = 0 ...
2
votes
0answers
66 views

How much advantage would a Blackjack player gain by being able to see the underside of cards?

In the novel Spaceland by Rudy Rucker, the protagonist Joe Cube is grafted with an eyestalk that sticks vout into the fourth dimension. This lets him see under and inside three-dimensional objects ...
6
votes
3answers
227 views

Why are the surreals considered “recreational” mathematics?

One of my college math professors once remarked to me that it was interesting that John Conway's two "biggest" contributions to math were both recreational: the Game of Life and the Surreals. No one, ...
1
vote
0answers
37 views

On a certain type of card game

Suppose two players are playing a card game, which is described as follow. Each player is allowed to construct their own decks of exactly $n$ cards with an additional repeatable card, where each ...
2
votes
0answers
102 views

Inserting +/- into 123456789…

I'm looking at a generalization of the problem of inserting + and/or - into the blocks $123456789$ and $987654321$ to create a formula for $100$, like this: $$123 - 45 - 67 + 89 = 100$$ $$9 - 8 + 7 ...
2
votes
2answers
70 views

A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?

I did not know what to search to see if this existed elsewhere. But, I could not find it. Here's the question, does there exist a continuously differentiable function, $f: [0,1] \rightarrow ...
4
votes
1answer
76 views

Expected number of clusters on chessboard

N distinct squares are selected uniformly at random on an MxM chessboard, what is the expected number of clusters? A cluster is a collection of squares which are connected sideways, not cornerwise.
2
votes
1answer
104 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
90 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
269 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 ...
5
votes
1answer
74 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
40 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
votes
2answers
82 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
102 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
393 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
100 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
160 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 ...
1
vote
2answers
57 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
64 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
76 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
votes
0answers
63 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
142 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
109 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
0answers
43 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
votes
1answer
66 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
57 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
vote
1answer
187 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
58 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 ...
0
votes
1answer
94 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
71 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
66 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
vote
1answer
849 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
77 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
votes
2answers
191 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
89 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
60 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
votes
2answers
193 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
votes
1answer
149 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
74 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
103 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 ...
-1
votes
2answers
111 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
54 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 ...