Questions tagged [recreational-mathematics]

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

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66
votes
7answers
65k views

What is the math behind the game Spot It?

I just purchased the game Spot It. As per this site, the structure of the game is as follows: Game has 55 round playing cards. Each card has eight randomly placed symbols. There are a total of 50 ...
13
votes
2answers
1k views

Mathematics Behind the 4×4 and 5×5 Rubik's Cube

A lot is known about the math behind the 3×3 Rubik's cube (symmetries, generators, group structure etc...). Is the same true for the 4×4 and 5×5 cubes? I haven't had much success finding this ...
160
votes
6answers
27k views

Deleting any digit yields a prime… is there a name for this?

My son likes his grilled cheese sandwich cut into various numbers, the number depends on his mood. His mother won't indulge his requests, but I often will. Here is the day he wanted 100: But ...
11
votes
1answer
1k views

Solving a scrambled $3 \times 3 \times 3$ Rubik's Cube with at most 20 moves!

I read somewhere that any scrambled form of $3 \times 3 \times 3$ Rubik's cube can be solved using at most $20$ moves, and I just said "wow"! I am wondering can we prove this by mathematical ways? Or ...
14
votes
2answers
1k views

any pattern here ? (revised 2)

for any positive number $k$, I have a $(k+1)*(k+1)$ matrix. I wonder if these matrices follow any "obvious" pattern. My goal is to guess the elements for matrix with $k=5$ and above (most probably in ...
3
votes
2answers
1k views

Decryption Problem

The following message was posted in our math department and I wouldn't mind some help into getting started at cracking it: gectl atnoy danwm etaim oroni snair ohass wveno faome nceto kils Any ...
6
votes
1answer
1k views

How many steps does it take the computer to solve a Sudoku puzzle?

We all know what Sudoku is. Given a Sudoku puzzle, one can use a simple recursive procedure to solve it using a computer. Before describing the algorithm, we make some definitions. A partial solution ...
33
votes
3answers
2k views

For which number does multiplying it by 99 add a 1 to each end of its decimal representation?

This was asked by my maths lecturer a couple of years ago and ive been wracking my brains ever since: Find a number that, when multiplied by 99 will give the original number but with a 1 at the ...
13
votes
1answer
529 views

Fewest required values in magic square?

A magic square of order $n$ is an $n \times n$ grid containing each of the numbers $1,2,\dots,n^2$, so that the numbers in each row, column, and diagonal sum to the same number $n(n^2+1)/2$. This ...
11
votes
1answer
4k views

What are the 2125922464947725402112000 symmetries of a Rubik's Cube?

In a recent talk, Marcus du Sautoy says there are 2125922464947725402112000 (2.1*10^24) symmetries of a Rubik's cube, but doesn't explicitly identify what qualifies as a symmetry. What counts as a ...
13
votes
1answer
421 views

Behaviour of the series $\exp_p(x)=\sum_{k=0}^{\infty}\frac{x^k}{(k!)^p}$ depending on $p\approx 2$?

Note:This is more a math-recreational question Consider the series $\exp_p(x)=\sum_{k=0}^{\infty}\frac{x^k}{(k!)^p}$ which is some systematic modification of the exponential function. It's $\exp_1(x)=...
5
votes
2answers
406 views

Natural set to express any natural number as sum of two in the set

Any natural number can be expressed as the sum of three triangular numbers, or as four square numbers. The natural analog for expressing numbers as the sum of two others would apparently be the sum ...
4
votes
1answer
328 views

Is there any mathematical trick?

Given two natural numbers I am supposed to reverse each of them and then sum them up and reverse the sum to get the final answer. For example if the numbers are $4358$ and $754$ then the answer ...
2
votes
4answers
10k views

Why does rearranging the pieces of this triangle illusion give a different area? [duplicate]

Possible Duplicate: How come 32.5 = 31.5?
16
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2answers
940 views

Rubik's cube interesting questions?

The upper bound for the number of moves required to solve a regular Rubik's cube has been shown to be 20. Two questions come to mind: Does this result have more general significance? What are the ...
37
votes
4answers
2k views

Which is bigger: $9^{9^{9^{9^{9^{9^{9^{9^{9^{9}}}}}}}}}$ or $9!!!!!!!!!$?

In my classes I sometimes have a contest concerning who can write the largest number in ten symbols. It almost never comes up, but I'm torn between two "best" answers: a stack of ten 9's (exponents) ...
2
votes
2answers
608 views

Determining odds in Blackjack

How do you determine the different odds in Blackjack? For example, what would be the difference in odds from using 1, 2, or 3 decks? Also, what would be the difference in odds if you shuffle the deck ...
1
vote
1answer
83 views

Knowing the time of arrival to point X

I have a bus that does A-------X------------------------B it goes at 10 hours from A, having: Speed at A sA = 10 m/s constant ...
22
votes
5answers
1k views

Fun math outreach/social activities

What are some great math social activities for students? I'm looking for things that bring people together with a "light" mathematical touch. The goal is to create a stronger mathematical community in ...
5
votes
4answers
2k views

Question about basic strategy in Blackjack

I was watching Beating Blackjack with Andy Bloch where he runs through the basic strategy charts that outline the best strategy with playing the game. Later he also talks about the methodologies to ...
10
votes
3answers
2k views

Optimal algorithm for finding the odd sphere with a balance scale

Say we have $N$ spheres indexed as $1,2,3,\dotsc, N$ such that all of them have identical weight apart from one. We have to determine which sphere has the odd weight using just a balance scale. We ...
19
votes
8answers
114k views

When the roulette has hit 5 reds why shouldn't I bet to black?

First some context, I'm not a mathematician, not even close (as you will soon see) I do grasp some things about it but in a need to know basis, so plain english answers are appreciated (too). I can't ...
26
votes
1answer
2k views

Going to the Movies!

I was looking at movie times today and was struck by the oddly-spaced showing times. For example, at the local Loew's Theater "Tron: Legacy 3D" (127 min.) is playing on two screens at the following ...
0
votes
1answer
2k views

Units of Hamming, and Euclidean distance

This is just a simple doubt I wanted to clear. I'm calculating the Hamming and Euclidean distance between two columns in a matrix, where each column is storing time information in seconds of when a ...
13
votes
3answers
5k views

Lights out game on hexagonal grid

I greatly enjoyed the Lights Out game described here (I am sorry I had to link to an older page because some wikidiot keeps deleting most of the page). Its mathematical analysis is here (it's just ...
9
votes
1answer
2k views

Can somebody explain the plate trick to me?

I learned of the plate trick via Wikipedia, which states that this is a demonstration of the fact that SU(2) double-covers SO(3). It also offers a link to an animation of the "belt trick" which is ...
36
votes
8answers
3k views

Quotient geometries known in popular culture, such as “flat torus = Asteroids video game”

In answering a question I mentioned the Asteroids video game as an example -- at one time, the canonical example -- of a locally flat geometry that is globally different from the Euclidean plane. It ...
5
votes
2answers
746 views

How many ways can I make six moves on a Rubik's cube?

I am writing a program to solve a Rubik's cube, and would like to know the answer to this question. There are 12 ways to make one move on a Rubik's cube. How many ways are there to make a sequence of ...
3
votes
1answer
701 views

A problem related to the number 1963

You are allowed to use +, -, / and * (plus, minus, division and multiplication) signs and bracketing. These signs you can put between the numbers 1963 to form mathematical expressions. You must put ...
8
votes
1answer
464 views

$\binom{n}{k} : \binom{n}{k+1} : \binom{n}{k+2} = a : b : c$

It is a rather surprising fact (to me, at least) that $\displaystyle \binom{14}{4} = 1001$; $\displaystyle \binom{14}{5} = 2002$; $\displaystyle \binom{14}{6} = 3003$. Actually, this is the only ...
3
votes
2answers
217 views

Five Fridays and Sundays on October

How to prove that if you take any 400 consecutive Octobers then exactly 14 % of those years have five Fridays and Sundays?
4
votes
2answers
385 views

How is done the calculation of the minimum number of movement to solve any configuration of Rubik's Cube?

I have read a few weeks ago that some mathematical researchers have discover that the minimum number of movements to solve any initial configuration of a Rubik's cube has been downsized to 20. How do ...
12
votes
2answers
741 views

How many disconnected graphs of the Rubik's cube exist?

Let us say that a Rubik's cube in a particular configuration is in a particular "state". All other configurations of this cube (other "states"), which can be achieved by rotations of the cube can be ...
4
votes
3answers
20k views

Formula(/How) to find 2 numbers that add together to give one number and times to give another

I have $2$ numbers $a, b$. I need a formula (or a how to) to find which $2$ numbers $c,d$ will add together to give a and times together to give $b$. So $c + d = a$ $c \cdot d = b$
14
votes
1answer
1k views

What's the probability that a sum of dice is prime?

Prompted by today's Minute Math question on the MAA site (http://amc.maa.org/mathclub/5-0,problems/T-problems/T-web,ia/2005web/tb05-12-ia.shtml), I started thinking about the probability that the sum ...
4
votes
2answers
405 views

a sequential game of dice

consider the following game: 10 dice are tossed and those showing 3 are more are retained. [those showing 2 or less are discarded.] the remaining dice are tossed again and those showing 4 or more are ...
5
votes
1answer
653 views

Interesting Taxicab Problem?

I came up with this problem after discussion of taxicab geometry in math class... I thought it was a simple problem, but still pretty neat; however, I am as of yet unsure of whether my answer is ...
5
votes
2answers
2k views

Is this version of the Hanoi towers problem NP-complete?

This was really inspired by Solitaire, but a few people reacted with ``oh, it's like the towers of Hanoi, isn't it?'' so I'll try to pose the problem in terms of discs here. Let's start. There are n ...
7
votes
2answers
436 views

Watchdog Problem

I just came up with this problem yesterday. Problem: Assume there is an important segment of straight line AB that needs to be watched at all time. A watchdog can ...
61
votes
9answers
17k views

Where is the flaw in this “proof” that 1=2? (Derivative of repeated addition)

Consider the following: $1 = 1^2$ $2 + 2 = 2^2$ $3 + 3 + 3 = 3^2$ Therefore, $\underbrace{x + x + x + \ldots + x}_{x \textrm{ times}}= x^2$ Take the derivative of lhs and rhs and we get: $\...
8
votes
3answers
7k views

Optimal Strategy for Deal or No Deal

When I have watched Deal or No Deal (I try not to make a habit of it) I always do little sums in my head to work out if the banker is offering a good deal. Where odds drop below "evens" it's easy to ...
75
votes
9answers
20k views

Logic problem: Identifying poisoned wines out of a sample, minimizing test subjects with constraints

I just got out from my Math and Logic class with my friend. During the lecture, a well-known math/logic puzzle was presented: The King has $1000$ wines, $1$ of which is poisoned. He needs to ...
14
votes
3answers
3k views

Which books would you recommend about Recreational Mathematics?

By this I mean books with math puzzles and problems similar to the ones you would find in mathematical olympiads.
73
votes
7answers
8k views

How come $32.5 = 31.5$? (The “Missing Square” puzzle.)

Below is a visual proof (!) that $32.5 = 31.5$. How could that be? (As noted in a comment and answer, this is known as the "Missing Square" puzzle.)