All Questions
9
questions
4
votes
1
answer
380
views
What is the minimum number of squares to be drawn on a paper in order to obtain an 8x8 table divided into 64 unit squares? [closed]
What is the minimum number of squares to be drawn on a paper in order to obtain an $8\times8$ table divided into $64$ unit squares.
Notes:
-The squares to be drawn can be of any size.
-There ...
- 63
1
vote
0
answers
123
views
What is the best way to solve discrete divide and conquer recurrences?
Note: I have converted my announcement
into a question
and supplied an answer.
What is the best way to solve discrete divide and conquer recurrences?
The "Master Theorem" is one way.
What other ...
- 108k
0
votes
0
answers
46
views
Computing the cardinality of a combinatorial set
Define two sets: $S_1$ and $S_2$ where we have that $a$ is an odd natural number and $b\in \mathbb{N}$,
$S_1 = \Big\{ \frac{2}{a},\frac{2}{a-2},\frac{2}{a-4},...,\frac{2}{a-(a-1)},$
$\frac{2+4}{a+2},\...
user830143
4
votes
2
answers
195
views
Finding counterfeit coins
Suppose I have $N$ rare coins, of which $M \le N$ are counterfeits. I am blind. I ask an oracle who charges me a penny to tell me in yes/no answers whether there is a counterfeit in any group I show ...
- 555
4
votes
0
answers
310
views
Find the number of simple labeled graphs which have no isolated vertices
Find the number of simple labeled graphs on n vertices which have no isolated vertices? Compute the result for n=13
Total number of simple labeled graphs = $2^{n \choose 2}$.
How to remove vertices ...
- 860
4
votes
0
answers
95
views
partitions of finite set in same-size parts having at most one element in common
Given $g \ge 2$, $k \ge 1$ and a population of $p = kg$ workers, I'm trying to figure out the longest series of work shifts such that:
during each shift, all workers work in $k$ teams of g people;
...
- 257
3
votes
3
answers
354
views
why $m$ power by $n$ equals sum of $n$ numbrs
$$m^n=\sum_{i=0}^n(m-1)^i\binom{n}i$$
(a) I want to find a formula for the above and then prove it by induction. But there is two variable right those are $m$ and $n$. I know that this is true, ...
- 1,680
1
vote
1
answer
232
views
Minimum number of moves to change places of blocks.
There are $n$ blocks of O, X on each side of the board.
Board is one dimensional, $2n+1$ squares.
So it looks like this for $n=3$ case OOO*XXX (* is for an empty square)
a block may be moved into an ...
- 173
1
vote
2
answers
184
views
nth convolved Fibonacci numbers of order 6 modulo m
Problem: Find the coefficient of xk in (1−x−x2)-6 modulo m.
Constraints:
k≤264
m≤105, m can be a composite number.
I have 10^5 such queries to process in 2 sec, so O(log k) for each query ...
- 141