All Questions
17
questions
-1
votes
1
answer
54
views
I am getting an output on the computer from a formula which I am not able to understand
((n - Math.Abs(j / 2) - 1) * (n - Math.Abs(j / 2))) / 2 + i + 1
this line of code is giving output of 1 for values set
n=4;j=7;i=0
when i do manually on paper i am getting 0/3 =0 what am i doing wrong
...
- 101
2
votes
1
answer
136
views
Why are the catalan numbers giving the unique/correct patterns from all the combinations?
I am reading about catalan numbers and they are considered to represent the number of valid pair of parentesis, mountains etc.
Although the number checks out correct when comparing against specific ...
- 1,609
22
votes
1
answer
1k
views
Ways of choosing $16$ integers from first $150$ integers such that there is no $(a,b,c,d)$ for which $a+b=c+d$
Here is a problem I found out recently:
In how many ways one can choose $16$ distinct positive integers from first $150$ positive integers such that there are no $4$ distinct ones $(a,b,c,d)$ for ...
user916414
7
votes
2
answers
268
views
Erase every other number from $1, 2, 3, ... 2000$ until only one number left
One writes $1, 2, 3, ... 2000$ on the blackboard.
We erase every other number from left, so after one iteration we are left with $2, 4, ... 2000$
Then we erase every other number from right..
...
- 755
1
vote
0
answers
39
views
How limitations affect the number of possible pandigital numbers
First, I understand that the definition of "pandigital" can vary, somewhat, so for the purposes of this question, here's the definition we'll use:
"Positive and whole numbers that include each ...
- 125
1
vote
1
answer
123
views
Pascal-like Triangle Relation
I was fiddling around with an expansion, trying to find the coefficients of a certain formula, and I found that they satisfied the following relation for $0 \leq c \leq r$
$$
N(r,c) = \left\{ \begin{...
- 2,251
0
votes
1
answer
57
views
How do you sum a series when individual elements themselves may be series?
Okay Math SE, I've got a problem to fry your brains over. Let's see who can get this.
Consider this:
A cube exists in the euclidean space, it seemingly has the power to divide itself into a copy. ...
- 3
2
votes
3
answers
187
views
$\binom{28}{2}+\binom{28}{5}+\binom{28}{8}+\cdots+\binom{28}{26}=\frac{2}{3}(2^{27}+1)$
I need to prove the following identity
$$
\binom{28}{2}+\binom{28}{5}+\binom{28}{8}+\cdots+\binom{28}{26} = \frac{2}{3}(2^{27}+1).
$$
I have tried to use the fact that $\binom{m}{n}=\binom{m}{m-n}$ ...
- 279
1
vote
1
answer
9k
views
Number of 3 digit numbers with distinct digits
I need to find the number of 3 digit numbers without repetition (distinct digits).
MY ATTEMPT:
All 3-digit numbers:$100,101,102,103,.....,999$ (i.e. $1000$ numbers)
But we need to exclude following ...
user220382
6
votes
1
answer
131
views
Arrangement of houses with 2 colors
From the 2016 International Mathematical and Logic Games Contest
Along the coast of Maths-land, the straight beach-front
road contains a line of houses, all on the same side of the
road. The ...
- 35.9k
1
vote
1
answer
44
views
Number of way that set of point can be colinear
Assume I have $n$ points in a plane. and I want arrange them in the way that for any point at least I can find two other points that are all the three points are collinar.
I want to know how many way ...
- 1,769
26
votes
4
answers
517
views
How many ways are there to pile $n$ "$1\times 2$ rectangles" under some conditions?
A friend of mine taught me the following question. He said he created the question by himself and conjectured the answer, but couldn't prove it. Though I've tried to solve the question, I've been ...
- 145k
2
votes
1
answer
664
views
Sequences, sets and element position in the set.
I have a sequence Q with the length of N.
This is the fragment of this sequence:
68 70 72 74 76 78 80
The sequence has been divided into the sets of 4 elements ...
- 73
2
votes
1
answer
60
views
Number of Distinct Resistances that can be produced from n equal resistance resisters
Here is an interesting problem:
The number of distince resistances that can be produced from n equal resistance resisters is given below.
The Sequence
Surprisingly this is also equal to the number ...
user45099
1
vote
2
answers
992
views
Lengths of increasing/decreasing subsequences of a finite sequence of real numbers
Let $x_1,\ldots,x_n$ be a finite sequence of real numbers. Let $f(\{x_i\}_{i=1}^n)=f(\{x_i\})$ be the length of the largest non-decreasing subsequence, and let $g(\{x_i\})$ be the length of the ...
- 31.7k