All Questions
Tagged with combinatorics algorithms
1,042
questions
6
votes
1
answer
663
views
Balancing a Latin Square
I'm searching for an algorithm that forms a balanced (or quasi-complete) latin square, in which every element is a horizontal neighbor to every other element exactly twice, and a vertical neighbor to ...
- 81
9
votes
3
answers
9k
views
How can I (algorithmically) count the number of ways n m-sided dice can add up to a given number?
I am trying to identify the general case algorithm for counting the different ways dice can add to a given number. For instance, there are six ways to roll a seven with two 6-dice.
I've spent quite ...
- 557
4
votes
6
answers
5k
views
Finding the Heavy Coin by weighing twice
Suppose you have $100$ coins. $96$ of them are heavy and $4$ of them are light. Nothing is known regarding the proportion of their weights. You want to find at least one genuine (heavy) coin. You are ...
anonymous
12
votes
1
answer
830
views
Split up $n \in \mathbb{N}$ into sum of naturals with maximum LCM
Question:
Given some natural number, we can of course split it up into various sums of other naturals (e.g. $7 = 6 + 1 = 1 + 4 + 2 = \ldots$)
More precisely, for $n \in \mathbb{N}$, we can a find ...
- 2,624
4
votes
3
answers
301
views
Can this algorithm on removing $1$'s from a $(0,1)$-matrix fail?
Let us be given a $n\times n$ matrix containing only zeros and ones.Now, the goal is to remove some 'ones' from the matrix (i.e. replace them with zeros) so that in each row and each column there is ...
- 448
6
votes
5
answers
2k
views
Least wasteful use of stamps to achieve a given postage
You have sheets of $42$-cent stamps and
$29$-cent stamps, but you need at least
$\$3.20$ to mail a package. What is the
least amount you can make with the $42$-
and $29$-cent stamps that is ...
- 36.6k
16
votes
4
answers
5k
views
Is there a closed-form equation for $n!$? If not, why not?
I know that the Fibonacci sequence can be described via the Binet's formula.
However, I was wondering if there was a similar formula for $n!$.
Is this possible? If not, why not?
- 3,561