# Questions tagged [recreational-mathematics]

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

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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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" ...
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### 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 ...
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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
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### 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 $f(z)=g(z)h(z)=e^{-iz}(\cos(z)+i\sin(z))$, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $X_n$. ...
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### 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 ...
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### $5 \times 5\;$ “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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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: $x+y+z=338$ $xy+yz+zx=335$ ...
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### 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'...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...