Questions tagged [recreational-mathematics]

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

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7
votes
1answer
102 views

Tic-Tac-Toe on the Real Projective Plane is a trivial first-player win in three moves

Consider a $3 \times 3$ Tic-Tac-Toe board with opposite sides identified in opposite orientation. We play Tic-Tac-Toe in the Real Projective Plane. More precisely, consider a $3 \times 3$ Tic-Tac-Toe ...
7
votes
1answer
91 views

Odds of assembling a jigsaw puzzle “perfectly”

A bunch of my coworkers have gotten way into assembling jigsaw puzzles during the workday, so I got this idea it'd be fun to bore them with random facts. I'm trying to think of the odds of assembling ...
3
votes
1answer
73 views

Which even bases do self “dividing” numbers exist?

Define a self dividing number in base n to be a number n digits long such that The digits $0-9$(depending on base) is used exactly once The first h digits are divisible by h, for example in decimal ...
-1
votes
1answer
37 views

Any fun way applying concepts at home [closed]

Looking for fun ways to apply math concepts and play around with them, specifically using trigonometry, any suggestions?
1
vote
1answer
113 views

About IMC (Invitational international mathematics competition)

Last year I was invited to the international mathematics competition, however, I wasn't well prepared. Can you guys please recommend some books for me to read, in order to get better, at solving IMC ...
10
votes
1answer
470 views

A non-composite sequences

Can you provide a counterexample for a claim given below? Inspired by Puzzle 937 I have formulated the following claim: For any $n > 0$ let $B = p_1 \cdot p_2 \cdot .... \cdot p_n$ be the ...
6
votes
2answers
67 views

Writing on a paper- portrait or landscape?

For one of my exams I am allowed a one-sided equation sheet on a regular piece of printer paper. This got me thinking. If I write in rows, that is, I start at the top right and write until I get to ...
0
votes
1answer
62 views

Generations paradox [duplicate]

I have $2$ parents, $4$ grandparents, $8$ great grandparents, etc. So, going back $N$ generations, I have $2^N$ great...great grandparents. But $2^N$ is seriously divergent. I only have to go back ...
1
vote
2answers
76 views

What would be the best way to memorize the 10 by 10 multiplication table?

Hear me out before you start downvoting please. I have a learning disability so no matter how hard I try I can’t memorize the table. Please give some tips/hints on how to memorize the table. Thanks in ...
6
votes
1answer
63 views

Are these pointing sequences periodic?

A year or two ago I was fiddling around with sequences and I stumbled upon a family of sequences that seem to have some interesting properties. The family, $\mathcal{S}$, is defined as follows: $$ f\...
1
vote
2answers
59 views

How do I prove that $ex/\ln(x)$ is the function traced out by the successive functions?

Why is the purple function equal to $ex/\ln(x)?$ How do I prove this? After tracing out successive blue functions I wanted to find the function that passed through the minimum points of the ...
1
vote
0answers
40 views

Why don't we generalize rotation by rotating parallel to a plane instead of around a point or line?

When we learn about rotation, we are thought that in 2D you can rotate objects around a point and in 3D you can rotate things around a line. If we generalize this, then rotating an object in a $n$-D ...
0
votes
0answers
85 views

“New Year falls more often on Sundays than on Mondays”

This is a question from a hungarian math contest from the year 1948. It was Saturday on the 23rd October, 1948. Can one conclude that New Year falls more often on Sundays than on Mondays? Well, I ...
3
votes
3answers
225 views

Why 0.33… is the only expression of 1/3? [duplicate]

I am an undergraduate math student who loves mathematics very much, and I am confused by a math problem. Given $1/3$, we know that $0.33...$ (there are infinite $3$s) is the decimal expression. But ...
0
votes
1answer
33 views

Partially Non-Computable Numbers

Could there be a number say: A = $0.a_1a_2\cdots a_n$->$a_k \cdots$ where say {$a_1a_2$} and {$a_n$->$a_k$} are computable parts of A. Yet every thing else is not computational. I imagine a scheme ...
0
votes
1answer
97 views

Meaning of Maclaurin expansion of $e$

I was wondering if there is an interpretation or specific meaning to the series expansion of $e$. $$ e = \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \...
8
votes
0answers
167 views

Heesch numbers in 3D

At the Tiling Database there are 3, 20, 198, 1390 (A054361) non-tiling polyominoes of order 7 to 10. In 3D, solids with a particular Heesch number don't seem to be well known. Glenn Rhoads found ...
0
votes
2answers
50 views

How to compute the different number and ways to read a given phrase forming a pile or a stack?

I'm totally lost in this riddle, does it exist a way to calculate the different ways to read a word using a systematically approach?. In my initial attempt what I tried to do is drawing a circle over ...
0
votes
0answers
18 views

Combination of cards question

set of cards numbered 1 through 9. They shuffled their own cards and selected a card at random. If the numbers on their cards matched, they won. Wendy and Marc played this game once only. What is the ...
3
votes
1answer
111 views

Understanding solution to the secretary problem

I am trying to understand the solution to the Secretary Problem (see, e.g., Wikipedia: https://en.wikipedia.org/wiki/Secretary_problem). As I see it, it is usually solved in the following way: (1) It ...
0
votes
1answer
49 views

How to solve this problem raven matrices problem?

I am doing this free test in http://test.mensa.no/ That, as far as I know, the only problem I can't solve. Basically we shift the first row to the right. From first to second is easy transformation. ...
6
votes
0answers
63 views

Is this kind of “Gerrymandering” NP-complete?

Consider the following simplified form of "Gerrymandering": You have $n^2$ squares arranged as an $n\times n$ matrix. Each square is marked with either $0$ or $1$ which means a "voter preference" ...
2
votes
3answers
89 views

Two doors, each either trapped or safe, have signs whose truth depends on certain circumstances. Each sign reads “Both doors are safe”.

A friend of mine sent me the following puzzle: There are two doors, and behind them either a trap, or a safe passage to somewhere, and on the doors, it is written something about whether the ...
1
vote
2answers
63 views

Add the following numbers and find the answer?

Sum the $3$ numbers from the list $?+?+?=30$ Fill the boxes using $1,3,5,7,9,11,13,15$ You can also repeat the numbers
6
votes
1answer
113 views

What is the smallest number of $45^\circ$–$60^\circ$–$75^\circ$ triangles in non-trivial substitution tiling?

Let base = $45^\circ$–$60^\circ$–$75^\circ$ triangle. Over at What is the smallest number of bases that a square can be divided into? it was determined that 23 base were needed to make a $45^\circ$–$...
4
votes
0answers
46 views

An extension of $\mathbb{F}_p$ to an interval $[0,p]$ with $p \equiv 0$

I had a curious question bouncing around my head the other day. I asked myself if there were numbers with similarly nice properties to something like $e$ in a finite field, along the lines of $\mathbb{...
0
votes
1answer
47 views

Clever equalities proven similarly to Euler's Identity

From How to prove Euler's formula: $e^{i\varphi}=\cos(\varphi) +i\sin(\varphi)$?, a very elegant proof of Euler's Identity was given. Namely, observing $f(z)=g(z)h(z)=e^{-iz}(\cos(z)+i\sin(z))$, ...
0
votes
1answer
48 views

Find the odd one out

I've been trying to work this for a while and I believe the odd one is the 4th figure, but don't seem to find a satisfying justification for this. Any help? Few observations: 1) Bottom two dots ...
0
votes
1answer
38 views

Is it possible to calculate the height and distance of an object if the horizon is obstructed?

Basically, if I know $x$, $\theta_1$, and $\theta_2$ in the image below, it is possible to determine $h_1$ and $d$, or do I also need to know $h_2$ first? If the horizon is visible, then the ...
1
vote
1answer
97 views

How to win in Battleship?

Battleship explained in wiki: (also Battleships or Sea Battle1) is a guessing game for two players. It is played on ruled grids (paper or board) on which each players fleet of ships (including ...
6
votes
2answers
125 views

Distribution at First Time a Sum Reaches a Threshold

Consider the following problem. Roll a die many times, and stop when the total exceeds $M$, for some prescribed threshold $M$. Call this time $\tau$, and call the running score after $n$ rolls $X_n$. ...
1
vote
2answers
55 views

Proof or disproof of the existence of a way to flip all bits on a (undirected) graph

Suppose there is an undirected graph $G=(V,E)$. Each node $v\in V$ is allowed to be labelled either "$0$" or "$1$". Define an "operation" $f_v$ for each $v\in V$ which toggles the label for $v$ and ...
9
votes
0answers
401 views

$5 \times 5\;$ “square additive set”

Problem: IBM Research - Ponder This - January 2019 monthly contest (which was closed few days ago) leads to the problem: Find sets $A = \{a_1,a_2,\ldots,a_n\}$, $B = \{b_1,b_2,\ldots, b_m\}$ such ...
1
vote
1answer
49 views

Proof for a question regarding order of $n$-tuples of real numbers

Question as an image Let $x = (x_1, x_2, x_3,..., x_n)$ and $y= (y_1, y_2, y_3,..., y_n),$ where $x_1, x_2, x_3,..., x_n ,y_1, y_2, y_3,..., y_n$ are real numbers. We write $x > y$ if, for some $...
1
vote
2answers
55 views

Geometrical proof for length of chord passing through vertex of parabola

In a parabola $y^2=4ax$ , the length of focal chord making an angle $\theta$ with the x - axis is $4acosec^2\theta$ . If a chord is drawn parallel to that focal chord which passes through vertex of ...
0
votes
4answers
80 views

Linear equations applications

I'm reading Jane Eyre in class and we have to do questions. However, there are page numbers in the questions that relate to a different copy of the novel that I have. I was wondering if I could create ...
0
votes
1answer
25 views

Distributing a number over a course of time

Hi I want to know how to evenly distribute a cost evenly over a course of time between three people. the total cost of the fee is $160 dollars over 34 days. however, 2 out of the 3 people have been ...
0
votes
3answers
88 views

Math puzzles suitable for printing on a mug

I need to design a cup for a reception for first-year college students and i'm searching for some challenging and entertaining math puzzle or game to use. Previous years it has been used the "Three ...
5
votes
1answer
231 views

Five Similar Triangles from 4-5-6

A 4-5-6 triangle can be divided into 5 similar scalene triangles. I have the solution, but I figured out it was a 4-5-6 after putting together the component triangles. Can anyone else find it? The ...
0
votes
1answer
262 views

Why does momentum appear to be not conserved in this elastic collision?

Here's a bit of a fun physics paradox, which I will pose, and then answer below. (These ideas were inspired by Grant Sanderson's fascinating video on how the digits of $\pi$ are hidden within elastic ...
0
votes
2answers
55 views

Solving complicated system of equations:

I'm trying to solve this system of equations, and was wondering if there is any possible algebraic manipulation I can do to solve this question. Here are the equations: $x+y+z=338$ $xy+yz+zx=335$ ...
3
votes
1answer
208 views

Prove that $2019^{2018}+2020$ is divisible by at least three primes.

Prove that $2019^{2018}+2020$ is divisible by at least three primes. I try to use modular arithmetic, but I believe the only prime I can find is 11. This means I have to find one more factor, but I'...
4
votes
2answers
95 views

Suggestions of long and complex formulas/equations, for practicing memorization (It's my hobby.)

First, I'm not a mathematician; my hobby is mainly memorization. I want to practice math formulas and/or equations memorization. In that way, I'm looking for large and complex formulas or equations ...
2
votes
2answers
51 views

Problemsolving with weights and their labels

The problem is stated as follows: With a balance scale and six given weights; 1g, 2g, 3g, 4g, 5g and 6g, is it possible to make sure the labels on the weights are put on correctly only using the ...
0
votes
0answers
73 views

I'm a celeb get me outta here: optimal strategy to open locks

Suppose there are two 4 digit locks and a given and finite set $A$ of 4 digit tuples. Two elements of $A$ open the locks. What shall I do? Stick to the number or stick to the lock? I. Choose the ...
1
vote
1answer
43 views

Generating rotating groups for a seminar

One of my teachers is planning a seminar for his English class and he asked me if there was a way to generate the groups for the days other than brute-force random generating. I really think there ...
3
votes
1answer
67 views

Maximum number of ufo that can visit any planet

Consider an infinite alien 2d world consisting of infinite planet, so that distance between any two planets is not same. Now at some point of time, a ufo leaves each planet and goes to planet nearest ...
0
votes
1answer
20 views

Expected number of well addressed parcels

Consider the following mad postman scenario. The mad postman has $n$ parcels which should go to $n$ different destinations. However, the mad postman assigns destinations to the parcels randomly. What ...
2
votes
1answer
64 views

Candy machines and optimal strategy in terms of expected value

Problem We have three candy machines: call them G (good), B (bad) and M (mixed) . G always gives you a candy when you put 1\$. B never gives you a candy when you put 1\$. M gives you a candy with ...
1
vote
1answer
54 views

On which place should you stand in a line, to get a bonus.

Customers are going inside a store, the first customer whose birthday matches the birthday of someone that has already entered the store will get a bonus discount. Where on the line to stand to get ...