Combinatoric selections : Problem 53 Euler Project

Combinatoric selections :Problem 53

There are exactly ten ways of selecting three from five, 12345:

123, 124, 125, 134, 135, 145, 234, 235, 245, and 345

In combinatorics, we use the notation, ⁵C₃ = 10.
In general,

nCr =

n! r!(n−r)!

,where r ≤ n, n! = n×(n−1)×...×3×2×1, and 0! = 1.

It is not until n = 23, that a value exceeds one-million: ²³C₁₀ = 1144066.
How many, not necessarily distinct, values of  ⁿC_r, for 1 ≤ n ≤ 100, are greater than one-million?

Problem Source : Euler Project

Python Code:

 def combinatoricSelection():
    def binomial(n,k):
        if k < 2:
            if k == 1:
                return n
            else:
                return 1
        else:
            return (n*binomial(n-1,k-1))/k
   
    n = 23
    counter = 0
    for i in range(78):
        i = i + n
        for j in range (i):   
            if binomial(i,j) > 1000000:
                counter = counter + 1
    print counter               
combinatoricSelection()

Kaprekar's Number in JAVA: ISC Computer Science Practicals 2010

Given the two positive integers p and q, where p < q. Write a program to determine how

many kaprekar numbers are there in the range between 'p' and 'q'(both inclusive) and

output them.

About 'kaprekar' number:

SAMPLE DATA:

INPUT:

p=1

Q=1000

OUTPUT:

THE KAPREKAR NUMBERS ARE:

1, 9, 45, 55, 99, 297, 703, 999

FREQUENCY OF KAPREKAR NUMBERS IS:8

/* ISC COMPUTER SCIENCE PRACTICALS SOLVED, 2010 */