Applications of mathematics for the design and analysis of games and puzzles
Questions tagged [recreational-mathematics]
290 questions
15
votes
12 answers
Alternatives to pi day
If you don't already know, pi day happens on March 14 (3-14) every year. Festivities include reciting digits of pi and eating pies. I understand that it's all in good fun, but I've always felt that pi day is bad PR for mathematics. To…
Anton Geraschenko
- 23,718
11
votes
1 answer
Do there exist associative sudoku squares?
Last night I taught an algebra tutorial, and while writing out the multiplication table for the units of $\mathbb{Z}/5\mathbb{Z}$, a student remarked that it looked like a sudoku puzzle. I noted that it was similar, as the rows and columns all…
cfranc
- 333
8
votes
2 answers
The motorcyclist's challenge
n walkers ${A}_{i}$ start out from X to Y simultaneously with speeds ${a}_{i}$, $i=1,2,...,n$. ${a}_{i}\neq {a}_{j}$ if $i\neq j$. At the same time, a motorcyclist M with speed $m=1$ starts out from Y to carry them (as shown in the illustration…
Eric
- 2,601
8
votes
2 answers
What are the possible numbers of regions that 4 planes can divide space?
What are the possible numbers of regions that 4 planes can create?
We know that the minimum number is 5 and the maximum number is 15.
(http://mathworld.wolfram.com/SpaceDivisionbyPlanes.html)
Is it possible to make a generalization based on the…
user9107
- 103
3
votes
2 answers
Game of Roller Blocks
The game of roller blocks is played on a rectangular board of size $m\times n$. For example, if $m=5$ and $n=4$ we have $5 \times 4=20$ different gridpoints/coordinates. Just so the conventions are clear, the lower-left corner can be written as…
SSequence
- 861
2
votes
2 answers
Critical thinking rail track problem
On a strange railway line, there is just one infinitely long track, so overtaking is impossible. Any time a train catches up to the one in front of it, they link up to form a single train moving at the speed of the slower train. At first, there are…
Alpha Gamma
- 61
1
vote
1 answer
Wrapping Wallpapers around Surfaces
I am intrigued by my honey bottle. Its neck is neatly wrapped by (almost) hexagons. I checked and there are no such things as part-hexagons, quarter-hexagons, half-hexagons, etc. -- if you have seen how floor tiles meet corners of walls you know…
Ye Tian
- 161
1
vote
0 answers
Multiplicative semi-magic squares
Magic squares (Wiki) and Multiplicative magic squares (Wiki) are famous.
In this question, let us suppose that we do not consider the diagonals of multiplicative magic squares. Let us call such mulitplicative magic squares "multiplicative…
mathlove
- 4,727
1
vote
1 answer
2D visualization of sum of divisors using Cantor pairing
Related to Gerhard's question about ascii plots. On the SeqFan mailing list
was suggested to plot an
integer sequence this way:
Let $F(x,y)= (x+y) (x+y+1)/2+y$ be the Cantor pairing.
To plot an integer sequence $a(n)$, for a point $(x,y)$ compute…
joro
- 24,174
1
vote
1 answer
Nonexistence of high dimensional perfect magic hypercubes of fixed side length
I apologize in advance if this question is not of sufficient level. Define a perfect magic hypercube of side length $k$ and dimension $n$ to be one in which the cells are filled with consecutive integers and the sum of numbers over cells in any…
user22202
- 548
0
votes
1 answer
length of 'digital' recurring expansion of rational number
Here's a question of a 'recreational' nature.
A similar question has already been posed for radix 10 in particular:
Integer division: the length of the repetitive sequence after the decimal point .
My question has been partly answered there;…
Rhubbarb
- 524
0
votes
0 answers
Breaking a number in two different ways
I am interested in knowing if there is a name for this process:
Suppose I have positive reals $a_1,a_2,\ldots, a_k, b_1,b_2,\ldots, b_m$ such that $\sum_{i=1}^k a_i = \sum_{j=1}^m b_j.$
Then, I can come up with a sequence $c_1,c_2,\ldots, c_l$…
Hedonist
- 1,269