Puzzles, curiosities, brain teasers and other mathematics done "just for fun".
1
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0answers
8 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 ...
4
votes
1answer
87 views
You are Johnny Depp!
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
26 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 ...
6
votes
2answers
139 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 ...
1
vote
0answers
49 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 ...
3
votes
1answer
76 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 ...
218
votes
12answers
68k 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
74 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
34 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
23 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
83 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
127 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
81 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
547 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
45 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!
23
votes
2answers
471 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
45 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
58 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
54 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
122 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
66 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
536 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?
0
votes
1answer
96 views
Combine the three numbers in each group to get the same result
Combine the three numbers in each group to get the same result in each of the three groups. You can use addition, subtraction, multiplication, division, and exponentiation.
Group 1: $2, ...
5
votes
3answers
79 views
palindromic squares of palindromes
This question is inspired by Google's recent programming competition (modified slightly for ease of exposition).
For a given $n$, one of the problems was to find all positive "fair" integers $k$ less ...
1
vote
2answers
40 views
Lengths of increasing/decreasing subsequences of a finite sequence of real numbers
Let $x_1,\ldots,x_n$ be a finite sequence of real numbers. Let $f(\{x_i\}_{i=1}^n)=f(\{x_i\})$ be the length of the largest non-decreasing subsequence, and let $g(\{x_i\})$ be the length of the ...
5
votes
3answers
149 views
Distribution of palindromic numbers
We all know what a palindromic number is, it is a number which is the same, independent from which side we read it, for example 101, 202, 33733,....
It is also clear that there are infinity many ...
5
votes
3answers
197 views
Prove that $n+1$ elements of a set will contain a co-prime pair
Suppose $P$ is a set of $n + 1$ integers selected from $1,2,3,...,2n + 1$. Then how can we show $P$ contains two coprime integers? The result holds if $P$ contains only $n$ integers??
Added Let ...
-3
votes
1answer
110 views
mathematical problem functional analysis : no approxiamation is required
What is the absolute value of the root in below question and what does it represent geometrically ,i had a few approaches leading to possible values to approximation and know the answers,but i also ...
3
votes
2answers
78 views
Recreational number theory problem
Suppose we have a positive integer $n$ that has exactly three distinct prime factors, say $p,q, r$. How can we find a formula for the number of positive integers $\leq n$ that are divisible by none of ...
2
votes
2answers
80 views
How to make a box which has the largest possible volume?
I have sheet metal in form of an equilateral triangle and I want to fold it to make a container for the screws. How should I cut and fold to make the a box with largest volume?
Basically I cut the ...
58
votes
4answers
1k views
Probability that a stick randomly broken in five places can form a tetrahedron
Randomly break a stick in five places.
Question: What is the probability that the resulting six pieces can form a tetrahedron?
Clearly satisfying the triangle inequality on each face is a necessary ...
13
votes
2answers
198 views
Evaluation of a 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 ...
3
votes
2answers
62 views
Number theory Exercise
for positive integer $n$, how can we show
$$ \sum_{d | n} \mu(d) d(d) = (-1)^{\omega(n)} $$
where $d(n)$ is number of positive divisors of $n$ and $mu(n)$ is $(-1)^{\omega(n)} $ if $n$ is square ...
0
votes
1answer
64 views
Recreational Puzzle
$n^{3}$ cubes are glued together to form one solid cube which is then hung in the air. As time proceeds, the most outer layer of this solid cube begins to dissolve and eventually those smaller cubes ...
6
votes
1answer
69 views
Question on Q&A's
My friend gave a fun problem to me that went as follows:
A. For how many of these questions is zero the answer?
B. For how many of these questions is one the answer?
C. For how many of ...
0
votes
1answer
29 views
Dividing an arbitrary $2-D$ shape with integer area into arbitrary shapes of unit area
The name explains it all. I searched for it in MSE and came across a similar [one] but more simpler1. I was interested to know if we can prove that, i.e., given an arbitrary shape (closed and ...
2
votes
1answer
55 views
License plate consisting of 4 letters and 4 numbers
While doing homework today, the following question popped into my head:
Can you easily calculate the amount of unique license plates consisting of 4 letters and 4 numbers in any order?
It doesn't ...
4
votes
2answers
116 views
Wolves and chicks puzzle
This problem is from the handheld video game, Professor Layton and the Curious Village.
I think the solution is very cool, but more than that, I want to know how to show that the minimum number of ...
0
votes
3answers
91 views
Intersection of chord with circle knowing the length and a point
Let's take a circle with radius R, and center in O (0, 0). We take on this circle a point A with coordinates xA and yA.
We know that point A is one of the endings of a chord with length l.
Which is ...
2
votes
2answers
139 views
How to form pairs in a group so that each element is coupled with each other only once
My question is derived from real life but I think it's a classic mathematical problem.
My uncle wants to organize a group activity with 12 people and wants to start by pairing each person with each ...
3
votes
1answer
102 views
Another puzzle with locks
There is a safe with three locks, like the ones in the hotel rooms that are opened with a "key" which is similar to a credit card. There are three keys, a correct one for one for each of the locks, ...
3
votes
2answers
121 views
Combinatorics riddle: keys and a safe
There are 8 crew members, The leading member wants that only a crew of 5 people or more could open a safe he bought, To each member he gave equal amount of keys, and locked the safe with several ...
3
votes
2answers
152 views
Some Interesting Properties of the number 142857
The number 142857 have such interesting properties.
It is the smallest number for which x, 2x, 3x, 4x, 5x, 6x all have the same digits(in different orders, of ...
0
votes
4answers
99 views
How to verify method used to solve integral was actually the fastest?
Is there any way to verify if the method I chose to integrate (by hand) was indeed fastest, or if there exists some better technique? Can a computer tell me or show me what the fastest method was, ...
0
votes
0answers
23 views
Permutations of 1 to 9 and subsequences [duplicate]
Arrange the numbers $1,2,...,9$ in such an order that no four of them appear (adjacently or otherwise ie as a subsequence) in ascending or descending order.
Show that there is no arrangement of the ...
0
votes
1answer
103 views
LOVES+LIVE=THERE. How many “loves” are “there”?
This is a problem from Mathematical Circles ( Chapter 0, Problem#17 ). It goes like this:-
The answer is that there are 95343 "loves" in "there".
Now, this is something that I am unable to ...
5
votes
1answer
132 views
Fun Math Topics, Activities, and Riddles
I'll be teaching college algebra this summer. Last summer when I taught the same course, I finished lectures early (thanks mainly to LaTeX's Beamer package). I want to fill these gaps this time ...
32
votes
2answers
662 views
Do all natural numbers have a nonzero multiple that is a palindrome in base 10?
Some natural numbers have a nonzero multiple that is a palindrome in base 10. For example, $106 \times 2 = 212$, which is a palindrome, and $29 \times 8 = 232$, which is also a palindrome.
Aside ...
3
votes
1answer
49 views
line of mathematicians guess their own hat color out of c colors
There is a common problem in which a long line of N mathematicians are each given a hat that is either red or blue. They cannot see their own hat but can see all in front of time and can hear any ...
0
votes
3answers
55 views
How to illustrate a large number [closed]
I hope this is an okay place to ask a question like this:) I am going to do a presentation and want to illustrate in a fun way how much 303000 ton waste per year is. In the presentation I want to ...
