Puzzles, curiosities, brain teasers and other mathematics done "just for fun".
5
votes
2answers
109 views
Determining the strength of an abstract army
Lets imagine we have two armies, represented by lists of pairs of positive numbers,
like this: [($attack1$,$defence1$),($a2$,$d2$)...($an$,$dn$)] face each other in combat. The rules of combat are ...
5
votes
1answer
199 views
“8 Dice arranged as a Cube” Face-Sum Problem
I found this here:
Sum Problem
Given eight dice. Build a $2\times 2\times2$ cube, so that the sum of the points on each side is the same.
$\hskip2.7in$
Here is one of 20 736 ...
3
votes
1answer
112 views
Triangle from a given rectangle
We are given a set of (marked) points in a 2D coordinate system and function $f(x,y)$ which counts number of points marked in the rectangle $(0 , 0), (x , y)$ - where $(0 , 0)$ if down-left corner, ...
2
votes
1answer
59 views
Checking Sudoku - sufficient sums
Are the following condition sufficient for checking if solution of Sudoku with (extended output) is valide :
sum of values in each row, column and subsquare is equal to 45 and
sum of squares of ...
2
votes
1answer
38 views
least number of planes intersecting a finite number of points in space, but not intersecting origin.
Let
$$\mathbb{R}^*=\mathbb{R}-\{0\}$$
and
$$N=\{0,...,n\}$$
and
$$\mathcal{M}=\{ A\subseteq \mathbb{R}^3\times\mathbb{R}^* \mid (\forall\mathbb{x}\in N^3:\mathbb{x}\ne 0)(\exists(\mathbb{a},d)\in ...
2
votes
1answer
94 views
What is the probability of rolling a 1 on the Catenative Doomsday Dice Cascader?
As seen here. Assume that each cascader bubble begins with a d6, as opposed to being determined by the prime bubble along with the number of cascader bubbles; the scene makes it ambiguous.
...
1
vote
1answer
85 views
How can I solve an Euler-Lagrange equation that satisfies certain conditions
The idea comes from a recreational math problem-- Place two identical coins side by side and roll one along the circumference of another without slipping, how many revolutions will the rolling coin ...
1
vote
1answer
83 views
Discrete Maths question
Show that $S=\{1,3,4,5,9\}$ is a difference set for $\Bbb Z_{11}$.
Identify the design produced from $S$ by the sets of the form $S+i$, $i \in\Bbb Z_{11}$.
1
vote
1answer
119 views
In how many ways ( using only whole numbers ) can we divide 49 into 6 parts so that we can obtain any number between 1 to 49?
The series which forms the basis of all the other series is:- 1,2,4,8,16,18.
Some other combinations are:- 1,2,3,7,14,22 ; 1,2,4,7,15,20 ; 1,2,4,8,13,21. However, I obtained the basic combination by ...
0
votes
1answer
70 views
total number of different mixes
Patient Age Avg Visits / Year
<1 year 7.5
1-4 years 3.0
5-14 years 1.8
15-24 years 1.7
25-44 years 2.6
45-64 years ...
0
votes
1answer
63 views
Compute Birthdate From Age
I have an interesting problem. I want to compute a birthdate (Month Date, Year) from a given age. I understand that subtracting the given age from the current date will supply the year of birth, but ...
0
votes
1answer
61 views
Gradually rising or falling numbers
I'm looking for a number series I can use for gradually rising or falling numbers. The number series should not be linear and should converge to a number at some point.
(Sorry I'm really scared of ...
0
votes
1answer
133 views
Find Volume of a Wineglass - a Slice
A spherical wineglass, known diameter, is brim full of wine. What is the width of any vertical parallel slice with a volume of 1/4 of the wine?
Assume that the height of the wineglass is known.
0
votes
1answer
53 views
What are the chances of having certain cards on certain turns if you draw one card each turn?
You have a sixty-card deck. It has:
3 Aa and 3 Ab cards (6 A cards)
4 B cards
4 C cards
4 Da and 2 Db cards (6 D cards)
14 Ea and 10 Eb cards (24 E cards)
At the begining of the game, you draw 7 ...
