Practical exams, Math and more…

Its over - the practical exams are finished. So here is the update:

4th of Feb:

I entered the examination hall trying to figure out possible worst case scenarios ( my experience with the highly inaccurate fractional weights during the physical balance experiment hasn’t been pleasant. ). I was shivering and I got experiment 10 - simple pendulum. I zoomed away and after 7 readings, submitted my paper. I am not going to write about that, doesn’t deserve space on this blog.

5th of Feb (i.e. today):

I entered the hall with an air of confidence around me. Well, it is the last time I do practicals in school so the nostalgia did bug me. I finished my salt analysis experiment in a jiffy. My salt was barium chloride and the yellow precipitate that is obtained when the salt solution is allowed to react with potassium chromate was striking. Anyway, I did my volumetric analysis experiment after that and I was asked to estimate the amount of oxalic acid in 1000 ml solution using a 0.02 M solution of KMnO4 (potassium permanganate). I got the result to be 6.3636 gram. Brilliant, its over !

Now, I solved a few sums in math over the past few days. Here are the hopefully ok solutions. The star highlight is the last problem. I found it on a newsgroup and considering someone mentioned Donald Knuth there, I was eager to see if I could solve “any” sum of this legend of a computer scientist. I need laminated pics of Knuth, Shannon and Dijkstra. Can someone point me to a source where I can find a framed pic of these pioneers ? Right, lets move to the math.

Question1:

Find the sum of the digits in 100! (100 factorial).

#!/usr/bin/python
#Author: Shriphani Palakodety
# ProjectEuler.net problem 20

def factorial(n):
	if n == 0:
		return 1
        else:
		return n * factorial(n-1)

def sumOfDigits(n):
	num = factorial(n)
	num_list = [ int(x) for x in str(num) ]
	return sum(num_list)

print sumOfDigits(100)

Divide the numbers 1 ** 2, 2**2 …… 50 ** 2 into 2 groups so that the difference between the sums of the elements of each group is either 0 or the minimum value possible.

#!/usr/bin/python
#Author: Shriphani Palakodety
#Donald Knuth's problem (i think)

def genNumList(n):
	num_list = []
	for i in range(0, n+1):
		num_list.append( i ** 2)
	return num_list

def pairMaker(num_list):
	list1 = num_list
	list2 = []
	for i in range(0, len(list1)-1):
		list2.append(list1[i])
		difference = abs(sum(list2) - sum(list1[i:]))
		yield (list1[i:], list2[:i], difference)

def commode(n):
	bullshit = [ x for x in pairMaker(genNumList(n)) ]
	diff_list = []
	for element in bullshit:
		diff_list.append(element[2])
	return (diff_list, bullshit)

def solution(n):
	i = commode(n)[0].index(min(commode(n)[0]))
	return commode(n)[1][i]	

print solution(50)

I found some more semantic filesystems material that I will read tomorrow. I’ve got 2 more euler problems which I am about to finish. Lots of work to do but there are only 24 hours in a day.