# Questions tagged [recreational-mathematics]

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

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7answers
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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
1answer
421 views

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 ...
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 ...
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.
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.)