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

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-1
votes
1answer
42 views

Possible mathematical finishes to the darts game 501

I was recently posed a question by a friend - How many possible finishes exist within the darts game 501 which include 3 (or more doubles) and using no more than 9 darts? For those unfamiliar ...
1
vote
1answer
62 views

Is there a proof that zero multiplied by infinity = a real number [duplicate]

Someone told me that $0\times \infty = 1$. I am baffled by this because I thought you cannot multiply by infinity because it isn't a real number. If you can, is it possible to explain how and give ...
1
vote
1answer
66 views

Why does strategy-stealing not work for Go?

The related Wikipedia article states: In Go passing is allowed. When the starting position is symmetrical (empty board, neither player has any points), this means that the first player could steal ...
0
votes
0answers
23 views

Bracket of 64 team tournament questions [on hold]

So, in a 64 team bracket, the total number of outcomes is $2^{63}$, as there are two outcomes for 63 games. In an effort to drop that number from 9,223,372,036,854,775,808 to something more ...
-11
votes
0answers
42 views

math question - 4,2 equal to what? [on hold]

if 3,75 equal to 10 and 7,50 is equal to 20, 4,2 is equal to what?
0
votes
0answers
75 views

What is Unknown Number? [migrated]

I found a very interesting question about numeric puzzles from web and I cannot access to answer! can anyone help me? What is unknown number? and what is the Pattern?
26
votes
1answer
741 views

X'mas Combinatorics

Inspired the various** algebraic X'mas greetings sent to me over the festive period, I thought I would try to devise one of my own. $$\Large ...
25
votes
5answers
2k views

Function whose third derivative is itself.

I'm looking for a function $f$, whose third derivative is $f$ itself, while the first derivative isn't. Is there any such function? Which one(s)? or How can we prove that there is none? Notes: ...
0
votes
0answers
35 views

How can i solve the below recursion? [on hold]

I was solving a question on Topcoder. Here's a link to the question I came up with following recursion: $f(l,i)=2*(f(l+1,i-2)+f(l,i-1))$ l -> number of long events i-> number of instant events ...
0
votes
1answer
114 views

Spirit of the holidays. [closed]

My teacher gave us this homework problem to do over the break, and said the solution should be incredibly obvious, but I can't seem to figure out where I should start...can anyone help?! ...
-4
votes
2answers
28 views

At the carnival there are 5 times as many elephants as camels , if there are a total of 54 elephants and camels , how many camels are there? [closed]

At the carnival there are 5 times as many elephants as camels. If there are a total of 54 elephants and camels, how many camels are there ?
4
votes
1answer
79 views

Analytic solutions to a simple math trick

As proven here $3816547290$ is the only positive integer in which every digit is used; each digit is used only once; the first $n$ digits are divisible by $n$, for $n=1,...,10$. ...
-6
votes
1answer
77 views

Why is it possible to find the birth year by subtracting one's age from 114?

I noticed that any person can find their birth year just by subtracting their age from the number $114$. For example, if I am $25$ years old then from $114-25=89$ I know the birth year is $1989 $. ...
4
votes
1answer
46 views

Puzzling Sequence

Today I was given a question that first I thought might be easy to solve but then no matter how hard I tried I couldn't solve it.(It's not really related to maths just some puzzle) if: $$ 9999=4\\ ...
1
vote
1answer
36 views

How to calculate 2-d plane from 3 4-d points?

I want to compute 3-d cross-sections of a pentatope (4-dimensional tetrahedron). The 3-d cross-sections will be calculated as: x+y+z+w=c C is a constant that I will vary to get different ...
1
vote
0answers
47 views

Where can Gaussian Elimination be used?

I have searched for this and came to know about it that it is traditionally used to solve linear equations, finding determinant, rank of matrix, inverse of matrix. There was a problem on codechef: ...
1
vote
1answer
70 views

subtle/annoying fallacious proofs [duplicate]

I've been invited to a maths themed Xmas after party. I need to prepare a selection of interesting, and relatively simple fallacious proofs which other guests will try and find the flaw in. I'm trying ...
1
vote
1answer
30 views

Solving a reaction-diffusion problem using Separation of Variables

$$U_{t} - D U_{xx}= -kU$$ where BC: $U_{x}(0,t)=0$, $U_{x}(l,t)=0$ where $0 < x < l$, $t > 0$ IC: $U(x,0)=A + B cos \big(\frac{2πx}{l}\big)$ where $ 0<x<l$ where $D$ and ...
0
votes
0answers
39 views

Maths to take a user chosen number to a predictable number

As part of simple card trick, I want to allow a user to choose a number between 1 and 100 and then ask them to do various maths to lead them to the same number so their choice becomes irrelevant. One ...
15
votes
1answer
558 views

The 'Unlock All Digits' Game

I challenged myself and thought of a new problem I tried to solve. Here are the rules : The goal is to 'unlock' all the numbers $0,1,2,3,4,5,6,7,8$ and $9$ When you start the game, the only number ...
2
votes
3answers
48 views

$n$ is twice the sum of squares of digits of $n$

Let $f(n)$ denote the sum of squares of digits of $n$, that is $$ f(10k+r) = \begin{cases} r^2 + f(k) &\text{for }10k+r \neq 0,\\ 0&\text{otherwise}. \end{cases} $$ I've found (while ...
15
votes
4answers
2k views

Solving 9 sons puzzle

The following math puzzle : ...
2
votes
1answer
23 views

Special Binary Relations/ Empty Relation, Universal Relation And identity Relation?

The universal relation U = A × A. (Correct me if I'm Wrong). I believe that the Universal Relation is an Equivalence Relation The empty relation E = ∅. From my understanding, a Empty relation on a non ...
0
votes
0answers
56 views

How to dissect the 11x11 square with 7x7 hole to get a square

Following shape needs to be cut into minimum amount of pieces to form a square Well, I can't find a solution better than to 8 pieces
3
votes
5answers
82 views

Find the number of all 3 digit numbers $n$ such that $S(S(n))=2$

For any natural number $n$ ,let $S(n)$ denote the sum of the digits of $n$.Find the number of all 3 digit numbers $n$ such that $S(S(n))=2$
2
votes
2answers
66 views

Santa is secretly deranged! or, how to hand-generate assignments for a gift exchange?

Consider a standard Secret Santa/gift exchange game draw. We have a pool of $n$ people, each of whom is supposed to be assigned another member of the pool to find a gift for, without the recipient ...
0
votes
1answer
51 views

Multiply large numbers

Consider the product $723145878987 \times599987871$. If I want to know that what would be sum of unit and tens digit of the result then Is there a trick that I could find it as fastly as possible?
-2
votes
1answer
67 views

I Need Help Cracking This Code. Can Anyone Do It? [closed]

To Quote the poster " I Will Provide One, And One List of Numbers Only. If you can make a function, that results in all 30 respectively, I shall provide 20 more, if they work, then my enigma is ...
3
votes
1answer
75 views

Can the wolves catch the hare?

Say you have 7 positions. 1 Hare and two Wolves in the following starting positions:    H o     o W   W  o   o The hare can take a step of size 2. The ...
1
vote
2answers
96 views

switch the colour until only one black square is left

Consider a standard chess board (8 × 8 squares). In each move, you pick one row or one column and switch the colours of all 8 squares (from black to white or from white to black). Is it possible to do ...
1
vote
2answers
67 views

How can the sniffer dog find the bag of drugs?

There are $n$ bags. In one of the bags are drugs. There is a dog that when given a group of bags, can tell whether there are drugs in the group or not. Each sniff counts as a "turn". What is the best ...
0
votes
1answer
40 views

Geometric Interpretation of Trigonometric Ratios

Is there a "good" geometric interpretation of trigonometric ratios for complex values? For example, we know that $$\cos(z)=\frac{e^{iz} + e^{-iz}}{2}$$ for all complex $z$ but is there a way to ...
0
votes
0answers
34 views

Calculating equal playing time in a soccer game with minimum number of changes.

I need to produce a formula that takes the following parameters: T = time of game in minutes p = number of players on field at one time s = number of substitute players Each of these is variable ...
1
vote
1answer
76 views

Cutting chocolate diagonally

Given is chocolate with rectangular pieces of size $a \times b$. If it will be cut diagonally, how many pieces will be splitted? If knife pass exactly by concatenating we assume there is no damage ...
0
votes
0answers
22 views

finding angle of spirals along with length of it's line at a certain point

I'm tying to calculate the angles (the angle between each line segment and a horizontal ray to the right blue) of spirals at a certain point along with figuring out the length of the other lines. see ...
6
votes
1answer
81 views

How Do I Find My Car

I have been discussing this problem with a coworker for a few days now and neither of us have made any headway on it. I would appreciate any help with a possible solution or maybe a suggestion of a ...
0
votes
0answers
30 views

$n$th number of concatenating consecutive integers [duplicate]

How do I find the nth digit of concatenating consecutive integers as in: $123456789101112131415161718\cdots$ where the $10th$ digit = 1$ , $11$th$ = 0$, $12$th $= 1$, $13$th $= 1$ $\cdots$ How do I ...
0
votes
1answer
37 views

Conditions for magic square.

So I've messing around with magic squares and something occured to me: Assume we have a nxn grid of numbers which respects the sum conditions of a magic square as in it has the appropriate column, ...
0
votes
2answers
35 views

Recreational chess questions based on the knights

I basically know whether the following statements are true, but I would like to know how they are proved. A knight kept anywhere on an empty chess board can not reach its adjacent square in exactly ...
0
votes
3answers
64 views

An recreational question on analysis

Alice and Bob ran a marathon ($26.2$ miles) with Alice running at a uniform $8$ minutes per mile pace and Bob running erratically, but taking exactly $8$ minutes and $1$ second to complete each mile ...
6
votes
1answer
67 views

Inequality: $(a^3+3b^2+5)(b^3+3c^2+5)(c^3+3a^2+5) \ge 27(a+b+c)^3$

Proving inequality for positive real $a,b,c > 0$: $$ (a^3+3b^2+5)(b^3+3c^2+5)(c^3+3a^2+5) \ge 27(a+b+c)^3$$
1
vote
3answers
86 views

Olympic elementary combinatorics problem

This is a problem taken from the regional selections of the Italian mathematical olympiads: A knight is placed on the bottom left corner of a $ 3\times3 $ chess board. In how many ways can you move ...
6
votes
3answers
157 views

Secret Santa Perfect Loop problem

(n) people put their name in a hat. Each person picks a name out of the hat to buy a gift for. If a person picks out themselves they put the name back into the hat. If the last person can only ...
0
votes
0answers
15 views

Basic examples of probabilistic method

I'm looking for a truly basic example of probabilistic method proof which could be presented without a board (i.e. speaking only), that is, even moderately complicated calculations are not allowed. ...
0
votes
0answers
24 views

Point of most theoretical potential moves in a game of Scrabble

I was recently playing a game of scrabble with a friend and the point difference all but ensured that I was going to lose (100+ points with one rack of tiles left, and no more in the "pot" and I ...
13
votes
1answer
251 views

Infinite prisoners with hats — is choice really needed?

The problem is this (recently asked about here): A countably infinite number of prisoners, each with an unknown and randomly assigned red or blue hat line up single file line. Each prisoner faces ...
5
votes
2answers
137 views

Prisoners Problem

We have an infinite number of prisoners enumerated $\{1, 2, \dots\}$, and on each prisoner there is a hat of either blue or red color. The $n$th prisoner sees the hats of prisoners $\{n+1, n+2, ...
7
votes
4answers
175 views

If $(x+\sqrt{x^2 + 1})(y+\sqrt{y^2 + 1})=p$, find $x+y$

I was given this factorization problem and I tried many things, but couldn't solve it. Can someone, please, give me a hint? If $(x+\sqrt{x^2 + 1})(y+\sqrt{y^2 + 1})=p$, find $x+y$. Here $x, y$ ...
12
votes
0answers
169 views

Sheldon Cooper Primes

On the $73^{\text{rd}}$ episode of the Big Bang Theory, Dr. Sheldon Cooper, an astrophysicist portrayed by Jim Parsons $(1973 - \stackrel{\text{hopefully}}{2073})$ revealed his favorite number to be ...
6
votes
2answers
161 views

What is the coefficient of $x^{25}$ in $(x^3 + x + 1)^{10}$?

Here's what I have so far on the off chance that my thinking is correct... So using Vieta's the coefficient of the $x^{25}$ should be $-(r_1r_2r_3r_4r_5+r_1r_3r_4r_5r_6+...+r_6r_7r_8r_9r_{10})$ Since ...