All Questions
33
questions
7
votes
1
answer
387
views
Robot moves from $(x,y)$ to $(x+y, y)$ or $(x,x+y)$
I was working on some coding related to this topic I found on Stack Overflow. This lead me to a math problem I thought would be interesting. I was wondering if one was given a starting point, what ...
- 71
5
votes
3
answers
5k
views
How many ways to reach $Nth$ number from starting point using any number steps between $1$ to $6$
In a board game, dice can roll either $1, 2, 3, 4, 5$ or $6$. The board has $N$ number of space. Every time of dice roll randomly, pawn moves forward exactly to dice rolled a number. Now the problem ...
- 63
5
votes
0
answers
121
views
Partition problem where partition are in increasing order.
For given $n$ and $S$, how many possible combinations are there such that:
$x_1 + x_2 + .. + x_n = S $ $\forall i, x_i \leq x_{i+1}$ $\&$ $x_i \geq 1$
For example, if $n$ = 3 and $S$ = 5, there ...
- 51
4
votes
1
answer
252
views
Maximum number of iterations of a simple algorithm
Suppose there is a 0-1 string of length n. We can perform the following operation on the string:
We can choose two zeros and invert the subsequence between them. The inversion includes the two zeros ...
- 65
3
votes
2
answers
191
views
Guaranteed graph labyrinth solving sequence
Starting from a vertex of an unknown, finite, strongly connected directed graph, we want to 'get out' (reach the vertex of the labyrinth called 'end'). Each vertex has two exits (edge which goes from ...
- 53
3
votes
1
answer
115
views
From three integers, choose any two and replace one of them with the two numbers' mean. Show that we can obtain equal integers.
Let $a, b, c$ be three distinct positive integer numbers on a whiteboard. At each step, I choose two of them and I replace one of the two numbers with their arithmetic mean.
For example: I choose $a, ...
- 1,768
3
votes
1
answer
808
views
number of derangements
In the normal derangement problem we have to count the number of derangement when each counter has just one correct house,what if some counters have shared houses.
A derangement of n numbers is a ...
- 315
3
votes
2
answers
160
views
Most efficient algorithm to distribute n n-bit strings among n people
We are given $n$ people, whom we identify with the elements of $[n]=\{1,\ldots,n\}$. We are also given a finite collection $\mathcal{K}$ of subsets of $[n]$. The problem is to (efficiently) ...
- 69
3
votes
1
answer
58
views
Finding a recursive definition and computing $B(10)$
For $n \geq 1$, let $B(n)$ be the number of ways to express $n$ as the sum of $1$s and $2$s, taking order into account. Thus $B(4) = 5$ because $4 = 1 + 1 + 1 + 1 = 1 + 1 + 2 = 1 + 2 + 1 = 2 + 1 + 1 = ...
- 139
3
votes
2
answers
194
views
Google Question: Number of ways to select sets such that n is pure
Consider a subset $S$ of positive integers.
A number in $S$ is considered pure with respect to $S$ if, starting from it, you can continue taking its rank in $S$, and get a number that is also in $S$, ...
- 315
3
votes
0
answers
461
views
Count number of m-subsets with xor = 0 [closed]
Given positive integers $n$ and $m$, count the $m$-subsets $S\subseteq[2^n - 1]$ such that the bitwise XOR of the members of $S$ is $0$, where as usual for any positive integer $k$ we let $[k]=\{1,2,\...
- 740
2
votes
4
answers
266
views
How many numbers are there for a $16*16$ matrix
Consider all matrixes with $1,0$ if all the numbers are $1$ we define $S=1$ and if all the numbers are $0$ then $S=0$ if non of them happened then we divide it into $4$,$2^{n-1}*2^{n-1}$ matrixes and ...
- 3,568
2
votes
2
answers
215
views
Combination/Permutation Question
I'm trying to solve a programming challenge, and I have narrowed down all the challenge to a combination/permutation problem.
I ended up with 5 possible scenarios, and I need to find all possible ...
- 141
2
votes
1
answer
293
views
Counting permutations, with additional restrictions
There are 10 slots and some marbles: 5 red, 3 blue, 2 green, how many ways can you fit those marbles into those slots?
Those marbles fit in 10!/(5! 3! 2!) ways
...
- 404
2
votes
1
answer
61
views
How can i distribute the money in the fewest movements? [closed]
I am trying to evenly distribute the total amount to each person involved.
For example I will use money.
Example 1
Person A has $20
Person B has $40
Person C has $60
So to make everything even ...
