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

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3
votes
1answer
22 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
18 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
41 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
68 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
29 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 ...
8
votes
5answers
140 views

Sources for mathematics outside the mathematics world

In this question I would like to ask you about material showing the uses (or occurrences) of mathematics in the everyday world. The aim is to encourage with it a group of young undergraduate ...
-1
votes
0answers
51 views

What to mathematics books to read? [closed]

What are the top 20 mathematics books you should read before you die? I am not necessarily looking for classicals like Principia Mathematica.
15
votes
1answer
555 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
47 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
22 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
54 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
78 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
60 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?
-1
votes
1answer
61 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
71 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
92 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
61 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
30 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
74 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
36 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
56 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 $a,b,c > 0$: $$ (a^3+3b^2+5)(b^3+3c^2+5)(c^3+3a^2+5) \ge 27(a+b+c)^3$$
-3
votes
1answer
141 views

SEVEN - NINE= EIGHT [closed]

Things are not always what they seem. What is true from one point of view may be false from another and vice-versa, and here is a puzzle to prove it. Despite the fact that every arithmetic teacher in ...
1
vote
3answers
83 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
144 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
14 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
246 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
135 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
158 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
142 views

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

Working on some contest problems and came across this question. 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 ...
1
vote
3answers
53 views

Combinatorial card game [duplicate]

There is a card game I've played before, where it goes as follows: You take a standard deck of cards, and shuffle them randomly. You then proceed by flipping each card and placing them down, ...
1
vote
0answers
26 views

Adding a factor to a ranking?

I have a ranking of 10 items from best to worst. Let's assume that the best is ranked 1 and the worst is ranked 10. Each item is ranked according to some rules that we cannot know so all we get is the ...
0
votes
0answers
24 views

making /adjusting a perodic signal given an equation

I know if I have the sin wave equation Asin(2pif*t+phase) I can increase/decrease/adjust the periodic frequency of the signal by changing f. But if I have the following equation below how can I also ...
18
votes
5answers
1k views

Puzzle of gold coins in the bag

At the end of Probability class, our professor gave us the following puzzle: There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of ...
0
votes
1answer
60 views

sequence get number in sequence from place in sequence

There is a sequence $$X = {1,1,1,1,1,1,1 \dots 2,2,2,2,2,2,2,2 \dots,3,3,3,3,3,3 \dots 4,4,4,4,4,4,4 \dots (k-1),(k-1),k}$$ So there are $(k)$ 1's, $(k-1)$ 2's and $(k-2)$ 3's and so on. Is there ...
1
vote
1answer
41 views

Tree recursive question: number of nodes and relationship with children

Suppose a given tree T has n1 nodes that have 1 child, n2 nodes that have 2 children, . . . , nm nodes that have m children and no node has more than m children, how many nodes have NO child are there ...
2
votes
3answers
60 views

Fun problem. Apparently $\prod_i(1-p_i) \geq 1 - \sum_ip_i$ with $p_i \in [0,1]$ is always true. But how to demonstrate it?

so, I want to demonstrate the validity of the following inequality: $$ \prod_i(1-p_i) \geq 1 - \sum_ip_i $$ with $p_i \in [0,1]$, it is always true, which it seems to be always the case if you test ...
3
votes
2answers
121 views

how to solve triangles count puzzle

Below is a puzzle of counting triangles.How to solve such puzzle ? source: http://gpuzzles.com/mind-teasers/how-many-triangles-challenge/?source=stackmath
0
votes
1answer
44 views

Which Snake fields can be played infinitely long?

Snake is a very old game for phones. Its a 'real time game', that means you have to make decisions fast. The rules are: You are a snake. You can move to the left, to the right or go straight ahead. ...
2
votes
1answer
42 views

How big can the deck get while still allowing this puzzle to be solvable?

Here's a classic puzzle (I think Martin Gardner talks about it somewhere, though I'm not sure exactly where): Alice and Bob are co-conspirators. Alice is dealt five random cards from a standard ...
0
votes
2answers
58 views

Combinatorics type

I have this problem: From a set of numbers, such as $\{1,2,3,4,5,6\}$, a new set is created containing all the possible single pairs. ie. $\{12,13,14,15,16,\ldots\}$. Another set contains all the ...