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

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3
votes
1answer
103 views

Eight queens problem, wondering about the non-unique solutions

I've done the code that generates all the solutions. But know I am suppose to filter out any redundant solutions based on symmetry and rotations. I have code for vertical symmetry, horizontal ...
3
votes
1answer
327 views

Does solving a Rubik's cube imply alignment?

Today, I got my hands on a Rubik's cube with text on it. It looks like this: Now, I would love to know whether solving the right cube will also always correctly align the text on the cube or ...
4
votes
1answer
223 views

Expressing any given number in the form of $x^y + y^x$

I was told by one of my friends that any given positive integer can be expressed in the form of $x^y + y^x$ where x & y are integers. For example: 17 = $2^3+3^2$ Surprisingly,this could be done ...
3
votes
1answer
1k views

Mathematical model for solving minesweeper situations

Suppose there's a minesweeper board like the following: 1 1 1 A B C Where A, B, C is an unrevealed square which could contain a mine. This can be represented ...
10
votes
4answers
1k views

Ten soldiers puzzle

This is a puzzle from one popular book called "The Man Who Counted: A Collection of Mathematical Adventures",author is Malba Tahan. How to arrange ten soldiers in five lines in such a way that each ...
20
votes
1answer
889 views

Expert Minesweeper Probability Question

This is just a question I thought of while playing minesweeper. I think that finding the solution might be kind of fun, so I'm sharing it with you guys. If you have no concept of what minesweeper is, ...
6
votes
4answers
290 views

How many ways can we place these ships on this board?

I want to find out how many ways we can arrange these ships on this field. I just have no idea how to go about solving this. So I bring it to the Pros! The board is an 8 by 8 Board. There are 5 ...
14
votes
2answers
782 views

Minimally inconsistent Sudoku puzzle

A sudoku puzzle is a partially filled $9\times 9$ grid with numbers $1,\ldots,9$ such that each column, each row, and each of the nine 3×3 sub-grids that compose the grid does not contain two of the ...
1
vote
4answers
323 views

Proof for divisibility rule for palindromic integers

I am studying for a test and came across this in my practice materials. I can prove it simply for some individual cases, but I don't know where to start to prove the full statement. Can you help me? ...
6
votes
1answer
6k views

How are Blackjack Basic Strategy tables calculated (What is the maths behind them)

Lets assume a very basic set of rules and table for them, these rules are unlikely to be seen in any casino and the reason is clear, there is only a 0.04% edge in favour of the casino, this could be ...
5
votes
5answers
6k views

How many bananas can a camel deliver without eating them all?

This is a fun puzzle I was assigned on the first day of highschool (over a decade ago). I just dug it up randomly from under my bed and thought I'd share it with the SE community. At the time, I ...
1
vote
1answer
354 views

The Game of Nim

A position in Nim consists of some piles of coins. Two players alternate, with each move removing a portion of one pile. The winner is the player who takes the last coin. Suppose that the starting ...
5
votes
2answers
204 views

Finding the largest set of integers over an interval where the sum of any 'k' elements is unique

Consider the set $(s_1, ..., s_N) \in S$, where all $s_i$ are positive integers selected from some interval $[M, L]$ and the sum of any $k$ integers in $S$ is required to be unique and to have a ...
4
votes
1answer
289 views

The “beach problem”: does anyone know it? or know how to solve it?

The following problem was given some years ago in the German computer-science contest for pupils ("Bundeswettbewerb Informatik"). It was originally wrapped in a story which I will briefly translate ...
5
votes
1answer
432 views

Space-filling polyhedra (or honeycomb) survey?

Is there a survey anywhere of space-filling polyhedra? MathWorld's article, space-filling polyhedron, mentions about 400 being seen in pre-1981 books and papers. Wikipedia mentions 28 convex uniform ...
4
votes
3answers
713 views

What is the highest number that can be got from 4383 by moving exactly 2 matches?

What is the highest number that can be got from 4383 by moving exactly 2 matches? Number 1 has got 2 matches, so I thought it will be 47831 as I remove two matches from second number (3), but it ...
1
vote
3answers
116 views

compare which two cube is the same

I am solving following problem: The problem states that on figure 1 there is shown a cube with three facets on which there is drawn three section(length). This cube was put on other facet and ...
2
votes
1answer
94 views

How determine largest reflected number

I was trying to determine maximum number from list of given integer in problem 8 here (page 5). So as you see, there are 5 written numbers on paper, and on the wall there is a hanging mirror. We ...
1
vote
3answers
219 views

Deconstructing $0^0$ [duplicate]

Possible Duplicate: Zero to zero power It is well known that $0^0$ is an indeterminate form. One way to see that is noticing that $$\lim_{x\to0^+}\;0^x = 0\quad,$$ yet, ...
2
votes
3answers
256 views

Squares on a checkerboard

How many squares of all sizes arise using an $n$-by-$n$ checkerboard? How many triangles of all sizes arise using a triangular grid with sides of length $n$ ?
2
votes
5answers
542 views

Conway's game of life variations

Is there any known two-dimensional Conway's game of life variation where each cell can not be just on/off but able to hold more states, maybe 4 or 5?
1
vote
1answer
122 views

Need help on proceding a paper about estimating numbers of sudoku

I was reading a paper that I found via spiked math (http://spikedmath.com/comics/424-the-numbers-quiz-solutions.png): http://www.afjarvis.staff.shef.ac.uk/sudoku/sudoku.pdf. I have problem ...
0
votes
1answer
78 views

Game statistics: Extracting interesting patterns out of users and level

I made a small game and in course of time collected fair amount of data between users and level The level chart is long (120 levels) but looks somewhat like this $$ \begin{array}{|c|c|} ...
75
votes
4answers
4k views

What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into?

What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into? The image below is a flawed example, from http://www.mathpuzzle.com/flawed456075.gif ...
3
votes
0answers
211 views

What is known about functions of type $f(n+1) = f(n)^ {f(n)}$?

Update : having looked at Knut's Double Arrow Notation ( Thank you DJC), it seems that this question is nothing more than a frivourless wondering that should be undertaken by whom ever wonders it, it ...
2
votes
1answer
175 views

Evenly dividing candy bar into $n$ pieces

I have 2 friends. We have one candybar and we want to divide it evenly. Unfortunately we don't have any way of accurately measuring and cutting the candybar. Therefore we are looking for a method ...
4
votes
2answers
641 views

Minimal number of solutions to a sudoku cube

A "Sudoku cube" is a 3x3x3 uncoloured Rubik's cube. In the solved state, each face has the digits 1 through 9 arranged in ascending rows from top to bottom, and all of the digits on a given face have ...
16
votes
1answer
431 views

Choosing points in fractions of the unit interval

How long a series of points in (0,1) can be chosen such that the first two are in different halves, the first three are in different thirds, ... the first $n$ are in different $n^{\text{th}}$s? My ...
6
votes
2answers
163 views

Why are the periods of these permutations often 1560?

I ran across a math puzzle that went like this: Consider the list $1,9,9,3, \cdots$ where the next entry is equal to the sum mod 10 of the prior 4. So the list begins $1,9,9,3,2,3,7,\cdots$. Will ...
5
votes
2answers
148 views

Avoiding matching first digit of $a^n$ with $b^n$

For any given pairs of positive integers $a$ and $b$, is it possible that the first digit of $a^n$ never matches the first digit of $b^n$ for any positive integer $n$? (If $a=2$ and $b=5$ the only ...
25
votes
2answers
1k views

Proof of recursive formula for “fusible numbers”

The set of fusible numbers is a fantastic set of rational numbers defined by a simple rule. The story is well told here but I'll repeat the definitions. It's the formula on slide 17 that I'm trying to ...
9
votes
1answer
207 views

Cube skeleton bindings

Imagine that you have a cube skeleton, like so: Further imagine that you have three rubber bands that you can loop through any of the faces. However, only one rubber band may go through any ...
18
votes
7answers
532 views

Contemporary Mathematical Columns in Magazines

In good old days, Scientific American was host to some legendary mathematical (and computer science) oriented columns that inspired generations of scientists and engineers. Douglas Hofstadter, Martin ...
2
votes
0answers
158 views

$n$ by $n$ Primally Magic Squares

(Again copied verbatim from a September 2009 thread I made.) A Primally Magic Square (PMS) is exactly like a traditional magic square with a change of criteria. Where a traditional magic square is ...
10
votes
3answers
422 views

a tiling puzzle/question

My teacher gave us a riddle that goes like this: You have a 7x7 square and 16 3x1 tiles. Of the 16 tiles, 15 are straight and 1 is crocked ("L" shaped). When you tile the square with these tiles you ...
3
votes
3answers
872 views

What is the importance of an integer sequence like the happy numbers?

I've been looking at the happy numbers which led me to the OEIS and showed me that there are many documented integer sequences. What I don't understand is the importance of these sequences. To me, the ...
26
votes
6answers
12k 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
541 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 ...
122
votes
6answers
22k 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 ...
6
votes
1answer
527 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 ...
15
votes
2answers
955 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
311 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
592 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 ...
31
votes
3answers
1k 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 ...
6
votes
1answer
280 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 ...
9
votes
1answer
2k 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 ...
4
votes
2answers
311 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
299 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
2k views