Puzzles, curiosities, brain teasers and other mathematics done "just for fun".
0
votes
1answer
29 views
Grand Prix Race- Differential Equations
Driver A has boon leading archrival B for a while by a steady 3 miles. Only 2 miles from the finish, driver A ran out of gas and decelerated thereafter at ta rate proportional to the square of his ...
3
votes
1answer
54 views
How Many Clock Hand Positions Swap to a Valid Position?
My wording will not be exactly clear, but this is what I remember.
Suppose you have a clock with minute and hour hands and you switch their places to form another correct time. How many such times ...
0
votes
2answers
44 views
Five digit re-write game
In the habit of factoring numbers, a notebook I bought had a five digit item number $77076$, which factors as $2^2 3^2 2141$, which may also be $9 \cdot 8564$, and in this form the count of digits is ...
2
votes
0answers
49 views
Symmetry between differentiation and integration [duplicate]
I want to make clear, that I am interested in the question: Why does integration need a bigger spectrum of functions than differentiation and not why integration is harder!!!
as experience told me, ...
0
votes
0answers
14 views
Comprehending change of (Galilean) basis
Everybody knows the Galilean transform
$\left[\begin{array}{cc}t' \\x' \\\end{array} \right]
= \left[\begin{array}{cc}1 & 0 \\v & 1\\\end{array} \right]
\left[\begin{array}{cc}t \\ x ...
4
votes
1answer
64 views
cake cutting puzzle: why do finitely many cuts suffice?
Puzzle from http://www2.maths.bris.ac.uk/~majwm/compendium/cakeslice.php
A piece of angle $x$ is cut from a cake, which is purple on top and yellow underneath, and turned upside down. Then another ...
1
vote
2answers
58 views
Expected number of pieces of a chessboard
If n squares are randomly removed from a $p \ \cdot \ q$ chessboard, what will be the expected number of pieces the chessboard is divided into?
Can anybody please provide how can I approach the ...
3
votes
1answer
63 views
Minimum number of coconuts
Three friends namely $A$, $B$ and $C$ collected coconuts with the help of monkey and fell asleep. At night, $A$ woke up and decided to have his share. He divided coconuts into three shares, gave the ...
2
votes
5answers
78 views
When will two cars pass each other
There was a question in my math text book the other day that stated:
$2$ cars each travelling at a constant velocity around a ring ,
complete exactly $4$ and $7$ rounds in one hour. If they start at ...
1
vote
1answer
97 views
Raise a number to the “y” power without using exponents.
This is kind of a spinoff on my question Divide by a number without dividing.
Can anyone think of some clever ways to raise any given number to any given power without using an exponent anywhere in ...
0
votes
4answers
156 views
Divide by a number without dividing.
Can anyone come up with a way to divide any given x by any given y without actually dividing?
For example to add any given x to any given y without adding you would just do:
$x-(-y)$
And to ...
2
votes
1answer
101 views
Deriving the 37-percent rule for dating
I am trying to prove the theoretical "37-percent rule" for dating. The setup, if I remember correctly, is this. Suppose that you will meet exactly $N$ potential mates in your life, and you will meet ...
2
votes
0answers
63 views
A photon in expanding Universe (a snail on a tree)
I want to know how far a snail can reach in expanding universe. It has a constant speed c = 1 and tree is expanding at speed $v= H_0 D$, with Hubble constant $H_0 = 1$. Here D(T) is the distance of ...
2
votes
3answers
141 views
$2^n-3^m=1 , m,n \in \mathbb N =?$
$2^n-3^m=1 , m,n \in \mathbb N =?$ my questions are:
do m,n exist?
are they finitely many $m,n$?
if there are infinitely many is there a way to describe them all?
Same question about $3^n-2^m=1 $, ...
0
votes
4answers
71 views
Simple Math Problem
A bat and ball cost \$1.10.
The bat costs a dollar more then the ball.
How much does the ball cost?
If this is not the correct place to ask a question like this please tell me and I will remove it ...
1
vote
1answer
71 views
Math Behind the Game “Quoridor”
I'm going to write an article for middle school students to introduce them to the game "quoridor".
Tha game certainly is interesting, but it will be great to add to the article some serious "math ...
7
votes
1answer
72 views
Topology of Forum Posts
Okay, so here's an interesting question regarding web forums. Let's say you have a typical forum, such as the comments section on a blog, or whatnot. Viewers can post comments in response to either ...
0
votes
1answer
94 views
total number of different mixes
Patient Age Avg Visits / Year
<1 year 7.5
1-4 years 3.0
5-14 years 1.8
15-24 years 1.7
25-44 years 2.6
45-64 years ...
1
vote
0answers
51 views
You are Johnny Depp 3!
An extension of this question.
As @Jared stated in his answer the solution is:
we assume that the head pirate chooses between multiple possible proposals that maximize his profit by rewarding ...
3
votes
1answer
74 views
65-card deck consisting of 13 ranks and 5 suits
** I FIGURED OUT 15 out of 16 cases. I don't understand the last case of RUNT. Anyone helps?
I recently went to a math event and one person presented a weird card deck, consisting of 13 ranks and 5 ...
1
vote
0answers
28 views
Truchet tiles on a cube [duplicate]
We randomly place copies of the tiles into faces of the flattened cube.
1.Find the probability that the circular arcs on the Truchet tiles will form one loop, two loops, three loops and four loops?
...
1
vote
1answer
75 views
Heighway dragon and twindragon relation
The Heighway dragon F is defined as the limit set for the iterated function system $\begin{cases}f_1(z)=\frac{1+i}2 z\\f_2(z)=1-\frac{1-i}2z\end{cases}\quad$ starting from the two points 0 and 1.
The ...
0
votes
1answer
125 views
Finding probability that a person gets $7$ when rolling a pair of dice
*I STILL DON'T GET THE ANSWERS PROVIDED. PLEASE HELP!
In a game, the participant rolls a pair of dice. If the result is a $7$, he wins. If the outcome is a number $n$ different from $7$, he continues ...
3
votes
1answer
96 views
Truchet tiles on a flattened cube
We randomly place copies of the tiles into faces of the flattened cube. 1.Find the probability that the circular arcs on the Truchet tiles will form one loop, two loops, three loops and four loops? ...
0
votes
0answers
20 views
finding the number of square we get when randomly put patterns into a given table [duplicate]
the image of the three tile patterns is here. [http://imageshack.us/photo/my-images/211/solpd.jpg/]
12
votes
2answers
190 views
A card game with no decisions
A friend showed me a mindless card game he plays, in which the initial state of the deck completely determines whether he wins or loses. The game is played as follows:
Shuffle a standard $52$ card ...
6
votes
2answers
255 views
You are Johnny Depp 2!
An extension of this question repeated below.
A band of 9 pirates have just finished their latest conquest -
looting, killing and sinking a ship. The loot amounts to 1000 gold
coins.
...
2
votes
1answer
42 views
Number of Distinct Resistances that can be produced from n equal resistance resisters
Here is an interesting problem:
The number of distince resistances that can be produced from n equal resistance resisters is given below.
The Sequence
Surprisingly this is also equal to the number ...
2
votes
1answer
34 views
Formula for adapting a number for cross reference
As a keen cyclist I'm trying to use the Allen Coggan Relative Power table that then relates your Relative Power 'score' to what category rider you are.
My question is that given rides/segments/hill ...
9
votes
2answers
377 views
9 pirates have to divide 1000 coins…
A band of 9 pirates have just finished their latest conquest - looting, killing and sinking a ship. The loot amounts to 1000 gold coins.
Arriving on a deserted island, they now have to split up the ...
1
vote
1answer
45 views
If we were to locate another intelligent lifeform, how could we then estimate the total number of intelligent lifeforms in the galaxy?
Given the vast size of the Milky Way, it is unlikely that we are the only intelligent lifeform to be found within it. Given that we only have one data point (the Earth), we are forced to use a long ...
7
votes
3answers
170 views
Blending Colors
Three one-gallon buckets of red, blue, and yellow paint are each two-thirds full. Without the ability to measure, is it possible to equally mix all of the paint through a finite sequence of pours ...
3
votes
1answer
115 views
Cutting a cube by plane cuts
This is an extension of a 3rd grade problem.
How many pieces can one get at most if one cut a unit cube with n plane cuts?
1,2,4,8, ???
And assuming cutting through an area 1 takes time t, what is ...
4
votes
1answer
94 views
Trisecting a paper using hand and without using a ruler or compass
This is a practical problem born while folding a paper.
We can bisect a paper by using only hand.
$\star$ Easy, fold it so that the two ends (of the length) coincide and press
the paper to get ...
299
votes
17answers
82k views
A “simple” 3rd grade problem…or is it?
So this is supposed to be really simple, and it's taken from the following picture:
I don't understand what's wrong with this question. I think the student answered the question wrong, yet my ...
5
votes
1answer
84 views
Tiling an $n\times n$ Grid
Given an $n\times n$ grid, and $2\times 2$ checkered tiles (white in the upper left and bottom right corners, and black in the upper right and bottom left corners), what is the smallest number of ...
0
votes
0answers
46 views
What's the difference between a 2-sided and 2-sided strip polytan
There are 14 2-sided tetratans and 13 2-sided strip tetratans. The sets are identical, except the square is missing in the strip version. My best guess is that for strips, no vertex can have an edge ...
2
votes
0answers
26 views
How to find the point in a closed geometrical figure which maximizes the “direct-line-of-sight function”
To expand upon the title, and put it in clear terms, I phrase the problem thusly:
Consider the interior of any continuous, closed, non-self-intersecting curve in the plane. (I'm not sure if I'm ...
0
votes
2answers
91 views
Is $f(x)f(y)=f(x+y)$ enough to determin $f$? [duplicate]
I had a discussion with a friend and there it came up the question whether $f(x)f(y)=f(x+y)$, $f(0)=1$ and the existence of $f'(x)$ implies that $f(x)=\exp(a x)$. This seems very reasonable but I ...
1
vote
2answers
148 views
Weather station brain teaser
I am living in a world where tomorrow will either rain or not rain. There are two independent weather stations (A,B) that can predict the chance of raining tomorrow with equal probability 3/5. They ...
-3
votes
0answers
88 views
Math glitch or did I do something wrong? [closed]
Suppose: $$a + b = c.$$ This can also be written as: $$4a - 3a + 4b - 3b = 4c - 3c.$$
After reorganising: $$4a + 4b - 4c = 3a + 3b - 3c.$$ Take the constants out of the brackets: $$4 \cdot (a+b-c) = 3 ...
30
votes
14answers
609 views
How to entertain a crowd with mathematics? [closed]
I am a high school student who follows a university level curriculum, and recently my teacher asked me to hold a short lecture to a crowd of about 100 people (mostly parents of my classmates and such, ...
1
vote
2answers
49 views
How can be done by the method of mathematical induction?
We are given that $P(x+1)-P(x)=2x+1$
We also know that $P(0)=1$
We want to prove that $P(2004)=(2004)^2 +1$
Can someone explain how can be solved with mathematical induction?
Thank you in advance!
29
votes
2answers
563 views
Predicting Real Numbers
Here is an astounding riddle that at first seems impossible to solve. I'm certain the axiom of choice is required in any solution, and I have an outline of one possible solution, but would like to ...
5
votes
0answers
49 views
Evaluation of a slow continued fraction
Puzzle question... I know how to solve it, and will post my solution if needed; but those who wish may participate in the spirit of coming up with elegant solutions rather than trying to teach me how ...
2
votes
1answer
66 views
A game involving points in the integer plane - who wins?
I am running a workshop on puzzles and problem solving over the weekend and thought that it might be a good idea to get people engaged by phrasing some interesting mathematical results in terms of ...
3
votes
2answers
65 views
Why does the strategy-stealing argument for tic-tac-toe work?
On the Wikipedia page for strategy-stealing arguments, there is an example of such an argument applied to tic-tac-toe:
A strategy-stealing argument for tic-tac-toe goes like this: suppose that the ...
5
votes
1answer
131 views
Does there exist a positive integer $n$ such that it will be twice of $n$ when its digits are reversed?
Does there exist a positive integer $n$ such that it will be twice of $n$ when its digits are reversed?
We define $f(n)=m$ where the digits of $m$ and $n$ are reverse.
Such as ...
1
vote
2answers
72 views
Gold Coins and a Balance
Suppose we know that exactly $1$ of $n$ gold coins is counterfeit, and weighs slightly less than the rest. The maximum number of weighings on a balance needed to identify the counterfeit coin can be ...
30
votes
1answer
550 views
Proving that $x$ is an integer, if the differences between any two of $x^{1919}$, $x^{1960}$, and $x^{2100}$ are integers
For a specific real number $x$, the difference between any two of $x^{1919}$, $x^{1960}$ , and $x^{2100}$ is always an integer. How would one prove that $x$ is an integer?
