# Questions tagged [recreational-mathematics]

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

3,324 questions
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### Second derivative of itself

I know the $\frac{d^2x}{dx^2}= 0$, since $dx/dx = 1 ...$ But by playing with some equations it is easy to get that $d^2f/dx^2=f''(x)$, so $d^2f=f''(x)dx^2$ and $df=f'(x)dx$, so $df^2=f'(x)^2dx^2$. ...
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### Number of permutations differing in at least $d$ spots in pairwise comparisons

A friend and I were thinking about this problem today but we were unable to come up with a solution. Problem: Consider the the numbers $S=\{1,\ldots,n\}$. Given $2\le d \le n$ what is the ...
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### Find the smallest $n$ such that the $n$-th prime $p_n \equiv 330 \mod n$.

Find the smallest $n > 1$ such that the $n$-th prime $p_n \equiv 330 \mod n$. I was investigating the remainders when the $n$-th prime is divided by $n$. For every positive integer $a < 330$, ...
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### How many people are there when the word “with” is used? [closed]

How many people are there is the following statement: "Bob with his family of 4..." Is it: a total of 4 (Bob + 3 members) or a total of 5 (Bob + 4 members) ?
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### When to apply negative sign when number is squared

I always had this confusion of when I need to apply the negative sign in the calculation. I understand that $(-1)^2 = 1$ however why isn't $-1^2 = 1$?
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### Version of Fitch Cheney's card trick

Fitch Cheney's card trick is well known. Alice picks five cards from a deck. Bob takes them, gives one back to Alice and arranges the other four in some order. Chuck then enters the room, looks at ...
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### Why do we not use letters as numbers? [closed]

To me, it seems like such a waste of energy to teach children a new set of symbols $(0,1,2.....)$ after they have learnt the alphabet. Why do we not replace $a=0$ and $b=2$ until $j=9$ and use the ...
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### Is there a way to narrow down the choices to the picture below given the price?

So I saw this post somewhere and I’m curious if there’s a way to narrow down the possible things a person did given the total price he/she add up among the things listed in the picture below. https://...
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### An order-6 configuration

Here's an example of an order $96_6$ configuration found by L.W. Berman. Every point has six lines, every line has six points. The unique 6,6 cage graph is bipartite and is a Levi graph for the ...
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### Long anti-arithmetic permutation

A permutation is a sequence $(a_1, \ldots, a_n)$ in which each number $1, \ldots, n$ appears precisely once. We call a sequence anti-arithmetic if there are no non-trivial arithmetic subsequences in ...
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### Generating all possible Domino tilings on a $4 \times 4$ grid

I have a task to write a program which generates all possible combinations of tiling domino on a $4 \times 4$ grid. I have found many articles about tilings, but it is for me quite difficult and I ...
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### How to colour the US map with Yellow, Green, Red and Blue to minimize the number of states with the color of Green

I want to colour the US (only the states) map with Yellow, Green, Red and Blue. I was wondering what would be the lowest number of states with the colour of Green. We can of course use the other ...
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### Hopping to infinity along a string of digits

Let $s$ be an infinite string of decimal digits, for example: \begin{array}{cccccccccc} s = 3 & 1 & 4 & 1 & 5 & 9 & 2 & 6 & 5 & 3 & \cdots \end{array} Consider ...
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### Generalizing tug-of-war puzzle

A puzzle at the end of a 3Blue1Brown video asks the following question (paraphrased): From a group of 20 people, you get to send one person to participate in a tug-of-war tournament. You don't care ...
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### Finding place of the nine digits

The nine digits 1, 2, 3, ... .., 9 are placed in the nine triangles of the attached figure in such a way that the digits around each circle add up as indicated. Calculate the value of N.
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### Dudeney’s solutions to haberdasher's problem exact measures of sections

What is the IG length if the side of the square is 1? I wonder if it is half of the square side. The triangle below represents the haberdasher's problem. version 2 version 1 (added after edit, here ...